1
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Das P, Leeb V, Knolle J, Knap M. Realizing Altermagnetism in Fermi-Hubbard Models with Ultracold Atoms. PHYSICAL REVIEW LETTERS 2024; 132:263402. [PMID: 38996311 DOI: 10.1103/physrevlett.132.263402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2023] [Accepted: 05/17/2024] [Indexed: 07/14/2024]
Abstract
Altermagnetism represents a type of collinear magnetism, that is in some aspects distinct from ferromagnetism and from conventional antiferromagnetism. In contrast to the latter, sublattices of opposite spin are related by spatial rotations and not only by translations and inversions. As a result, altermagnets have spin-split bands leading to unique experimental signatures. Here, we show theoretically how a d-wave altermagnetic phase can be realized with ultracold fermionic atoms in optical lattices. We propose an altermagnetic Hubbard model with anisotropic next-nearest neighbor hopping and obtain the Hartree-Fock phase diagram. The altermagnetic phase separates in a metallic and an insulating phase and is robust over a large parameter regime. We show that one of the defining characteristics of altermagnetism, the anisotropic spin transport, can be probed with trap-expansion experiments.
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Affiliation(s)
| | | | - Johannes Knolle
- Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 München, Germany
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
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2
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Wang B, Aidelsburger M, Dalibard J, Eckardt A, Goldman N. Cold-Atom Elevator: From Edge-State Injection to the Preparation of Fractional Chern Insulators. PHYSICAL REVIEW LETTERS 2024; 132:163402. [PMID: 38701474 DOI: 10.1103/physrevlett.132.163402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 03/12/2024] [Indexed: 05/05/2024]
Abstract
Optical box traps offer new possibilities for quantum-gas experiments. Building on their exquisite spatial and temporal control, we propose to engineer system-reservoir configurations using box traps, in view of preparing and manipulating topological atomic states in optical lattices. First, we consider the injection of particles from the reservoir to the system: this scenario is shown to be particularly well suited to activating energy-selective chiral edge currents, but also to prepare fractional Chern insulating ground states. Then, we devise a practical evaporative-cooling scheme to effectively cool down atomic gases into topological ground states. Our open-system approach to optical-lattice settings provides a new path for the investigation of ultracold quantum matter, including strongly correlated and topological phases.
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Affiliation(s)
- Botao Wang
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Monika Aidelsburger
- Faculty of Physics, Ludwig-Maximilians-Universität München, Schellingstr. 4, D-80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 Munich, Germany
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - André Eckardt
- Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Nathan Goldman
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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3
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Pasqualetti G, Bettermann O, Darkwah Oppong N, Ibarra-García-Padilla E, Dasgupta S, Scalettar RT, Hazzard KRA, Bloch I, Fölling S. Equation of State and Thermometry of the 2D SU(N) Fermi-Hubbard Model. PHYSICAL REVIEW LETTERS 2024; 132:083401. [PMID: 38457712 DOI: 10.1103/physrevlett.132.083401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Accepted: 01/09/2024] [Indexed: 03/10/2024]
Abstract
We characterize the equation of state (EoS) of the SU(N>2) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N=3, 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum Monte Carlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU(N) FHM.
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Affiliation(s)
- G Pasqualetti
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - O Bettermann
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - N Darkwah Oppong
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - E Ibarra-García-Padilla
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics, University of California, Davis, California 95616, USA
- Department of Physics and Astronomy, San José State University, San José, California 95192, USA
| | - S Dasgupta
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
| | - R T Scalettar
- Department of Physics, University of California, Davis, California 95616, USA
| | - K R A Hazzard
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics, University of California, Davis, California 95616, USA
| | - I Bloch
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - S Fölling
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
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4
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Jackson A, Kapourniotis T, Datta A. Accreditation of analogue quantum simulators. Proc Natl Acad Sci U S A 2024; 121:e2309627121. [PMID: 38294940 PMCID: PMC10861924 DOI: 10.1073/pnas.2309627121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Accepted: 12/05/2023] [Indexed: 02/02/2024] Open
Abstract
We present an accreditation protocol for analogue, i.e., continuous-time, quantum simulators. For a given simulation task, it provides an upper bound on the variation distance between the probability distributions at the output of an erroneous and error-free analogue quantum simulator. As its overheads are independent of the size and nature of the simulation, the protocol is ready for immediate usage and practical for the long term. It builds on the recent theoretical advances of strongly universal Hamiltonians and quantum accreditation as well as experimental progress toward the realization of programmable hybrid analogue-digital quantum simulators.
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Affiliation(s)
- Andrew Jackson
- Department of Physics, University of Warwick, CoventryCV4 7AL, United Kingdom
| | | | - Animesh Datta
- Department of Physics, University of Warwick, CoventryCV4 7AL, United Kingdom
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5
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Shen K, Sun K, Gelin MF, Zhao Y. Finite-Temperature Hole-Magnon Dynamics in an Antiferromagnet. J Phys Chem Lett 2024; 15:447-453. [PMID: 38189682 DOI: 10.1021/acs.jpclett.3c03298] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2024]
Abstract
Employing the numerically accurate multiple Davydov Ansatz in combination with the thermo-field dynamics approach, we delve into the interplay of the finite-temperature dynamics of holes and magnons in an antiferromagnet, which allows for scrutinizing previous predictions from the self-consistent Born approximation while offering, for the first time, accurate finite-temperature computation of detailed magnon dynamics as a response and a facilitator to the hole motion. The study also uncovers a pronounced temperature dependence of the magnon and hole populations, pointing to the feasibility of potential thermal manipulation and control of hole dynamics. Our methodology can be applied not only to the calculation of steady-state angular-resolved photoemission spectra but also to the simulation of femtosecond terahertz pump-probe and other nonlinear signals for the characterization of antiferromagnetic materials.
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Affiliation(s)
- Kaijun Shen
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore
| | - Kewei Sun
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Maxim F Gelin
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Yang Zhao
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore
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6
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Di Carli A, Parsonage C, La Rooij A, Koehn L, Ulm C, Duncan CW, Daley AJ, Haller E, Kuhr S. Commensurate and incommensurate 1D interacting quantum systems. Nat Commun 2024; 15:474. [PMID: 38212298 PMCID: PMC10784295 DOI: 10.1038/s41467-023-44610-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Accepted: 12/19/2023] [Indexed: 01/13/2024] Open
Abstract
Single-atom imaging resolution of many-body quantum systems in optical lattices is routinely achieved with quantum-gas microscopes. Key to their great versatility as quantum simulators is the ability to use engineered light potentials at the microscopic level. Here, we employ dynamically varying microscopic light potentials in a quantum-gas microscope to study commensurate and incommensurate 1D systems of interacting bosonic Rb atoms. Such incommensurate systems are analogous to doped insulating states that exhibit atom transport and compressibility. Initially, a commensurate system with unit filling and fixed atom number is prepared between two potential barriers. We deterministically create an incommensurate system by dynamically changing the position of the barriers such that the number of available lattice sites is reduced while retaining the atom number. Our systems are characterised by measuring the distribution of particles and holes as a function of the lattice filling, and interaction strength, and we probe the particle mobility by applying a bias potential. Our work provides the foundation for preparation of low-entropy states with controlled filling in optical-lattice experiments.
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Affiliation(s)
- Andrea Di Carli
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Christopher Parsonage
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Arthur La Rooij
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Lennart Koehn
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Clemens Ulm
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Callum W Duncan
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Andrew J Daley
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Elmar Haller
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Stefan Kuhr
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom.
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7
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Wang WO, Ding JK, Schattner Y, Huang EW, Moritz B, Devereaux TP. The Wiedemann-Franz law in doped Mott insulators without quasiparticles. Science 2023; 382:1070-1073. [PMID: 38033050 DOI: 10.1126/science.ade3232] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Accepted: 10/27/2023] [Indexed: 12/02/2023]
Abstract
Many metallic quantum materials display anomalous transport phenomena that defy a Fermi liquid description. Here, we use numerical methods to calculate thermal and charge transport in the doped Hubbard model and observe a crossover separating high- and low-temperature behaviors. Distinct from the behavior at high temperatures, the Lorenz number [Formula: see text] becomes weakly doping dependent and less sensitive to parameters at low temperatures. At the lowest numerically accessible temperatures, [Formula: see text] roughly approaches the Wiedemann-Franz constant [Formula: see text], even in a doped Mott insulator that lacks well-defined quasiparticles. Decomposing the energy current operator indicates a compensation between kinetic and potential contributions, which may help to clarify the interpretation of transport experiments beyond Boltzmann theory in strongly correlated metals.
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Affiliation(s)
- Wen O Wang
- Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
| | - Jixun K Ding
- Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
| | - Yoni Schattner
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
- Department of Physics, Stanford University, Stanford, CA 94305, USA
- AWS Center for Quantum Computing, Pasadena, CA 91125, USA
| | - Edwin W Huang
- Department of Physics and Institute of Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
- Department of Physics and Astronomy, University of Notre Dame, Notre Dame, IN 46556, USA
- Stavropoulos Center for Complex Quantum Matter, University of Notre Dame, Notre Dame, IN 46556, USA
| | - Brian Moritz
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
| | - Thomas P Devereaux
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
- Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA
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8
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Abdelshafy M, Rigol M. L-based numerical linked cluster expansion for square lattice models. Phys Rev E 2023; 108:034126. [PMID: 37849211 DOI: 10.1103/physreve.108.034126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2023] [Accepted: 09/13/2023] [Indexed: 10/19/2023]
Abstract
We introduce a numerical linked cluster expansion for square-lattice models whose building block is an L-shape cluster. For the spin-1/2 models studied in this work, we find that this expansion exhibits a similar or better convergence of the bare sums than that of the (larger) square-shaped clusters and can be used with resummation techniques (like the site- and bond-based expansions) to obtain results at even lower temperatures. We compare the performance of weak- and strong-embedding versions of this expansion in various spin-1/2 models and show that the strong-embedding version is preferable because of its convergence properties and lower computational cost. Finally, we show that the expansion based on the L-shape cluster can be naturally used to study properties of lattice models that smoothly connect the square and triangular lattice geometries.
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Affiliation(s)
- Mahmoud Abdelshafy
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Marcos Rigol
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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9
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Janković V, Vučičević J. Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice. J Chem Phys 2023; 158:044108. [PMID: 36725525 DOI: 10.1063/5.0133597] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
Ultracold-atom simulations of the Hubbard model provide insights into the character of charge and spin correlations in and out of equilibrium. The corresponding numerical simulations, on the other hand, remain a significant challenge. We build on recent progress in the quantum Monte Carlo (QMC) simulation of electrons in continuous space and apply similar ideas to the square-lattice Hubbard model. We devise and benchmark two discrete-time QMC methods, namely the fermionic-propagator QMC (FPQMC) and the alternating-basis QMC (ABQMC). In FPQMC, the time evolution is represented by snapshots in real space, whereas the snapshots in ABQMC alternate between real and reciprocal space. The methods may be applied to study equilibrium properties within the grand-canonical or canonical ensemble, external field quenches, and even the evolution of pure states. Various real-space/reciprocal-space correlation functions are also within their reach. Both methods deal with matrices of size equal to the number of particles (thus independent of the number of orbitals or time slices), which allows for cheap updates. We benchmark the methods in relevant setups. In equilibrium, the FPQMC method is found to have an excellent average sign and, in some cases, yields correct results even with poor imaginary-time discretization. ABQMC has a significantly worse average sign, but also produces good results. Out of equilibrium, FPQMC suffers from a strong dynamical sign problem. On the contrary, in ABQMC, the sign problem is not time-dependent. Using ABQMC, we compute survival probabilities for several experimentally relevant pure states.
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Affiliation(s)
- Veljko Janković
- Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
| | - Jakša Vučičević
- Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
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10
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Yan ZZ, Spar BM, Prichard ML, Chi S, Wei HT, Ibarra-García-Padilla E, Hazzard KRA, Bakr WS. Two-Dimensional Programmable Tweezer Arrays of Fermions. PHYSICAL REVIEW LETTERS 2022; 129:123201. [PMID: 36179199 DOI: 10.1103/physrevlett.129.123201] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Revised: 06/27/2022] [Accepted: 07/29/2022] [Indexed: 06/16/2023]
Abstract
We prepare high-filling two-component arrays of tens of fermionic ^{6}Li atoms in optical tweezers, with the atoms in the ground motional state of each tweezer. Using a stroboscopic technique, we configure the arrays in various two-dimensional geometries with negligible Floquet heating. A full spin- and density-resolved readout of individual sites allows us to postselect near-zero entropy initial states for fermionic quantum simulation. We prepare a correlated state in a two-by-two tunnel-coupled Hubbard plaquette, demonstrating all the building blocks for realizing a programmable fermionic quantum simulator.
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Affiliation(s)
- Zoe Z Yan
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Benjamin M Spar
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Max L Prichard
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Sungjae Chi
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Hao-Tian Wei
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Eduardo Ibarra-García-Padilla
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Kaden R A Hazzard
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Waseem S Bakr
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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11
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Lenihan C, Kim AJ, Šimkovic F, Kozik E. Evaluating Second-Order Phase Transitions with Diagrammatic Monte Carlo: Néel Transition in the Doped Three-Dimensional Hubbard Model. PHYSICAL REVIEW LETTERS 2022; 129:107202. [PMID: 36112452 DOI: 10.1103/physrevlett.129.107202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2021] [Accepted: 07/25/2022] [Indexed: 06/15/2023]
Abstract
Diagrammatic Monte Carlo-the technique for the numerically exact summation of all Feynman diagrams to high orders-offers a unique unbiased probe of continuous phase transitions. Being formulated directly in the thermodynamic limit, the diagrammatic series is bound to diverge and is not resummable at the transition due to the nonanalyticity of physical observables. This enables the detection of the transition with controlled error bars from an analysis of the series coefficients alone, avoiding the challenge of evaluating physical observables near the transition. We demonstrate this technique by the example of the Néel transition in the 3D Hubbard model. At half filling and higher temperatures, the method matches the accuracy of state-of-the-art finite-size techniques, but surpasses it at low temperatures and allows us to map the phase diagram in the doped regime, where finite-size techniques struggle from the fermion sign problem. At low temperatures and sufficient doping, the transition to an incommensurate spin density wave state is observed.
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Affiliation(s)
- Connor Lenihan
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - Aaram J Kim
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
- Department of Physics, University of Fribourg, Chemin du Musée 3, 1700 Fribourg, Switzerland
| | - Fedor Šimkovic
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
- CPHT, CNRS, École Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
| | - Evgeny Kozik
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
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12
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Wei D, Rubio-Abadal A, Ye B, Machado F, Kemp J, Srakaew K, Hollerith S, Rui J, Gopalakrishnan S, Yao NY, Bloch I, Zeiher J. Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion. Science 2022; 376:716-720. [PMID: 35549436 DOI: 10.1126/science.abk2397] [Citation(s) in RCA: 30] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of a wealth of classical stochastic models. Surprisingly, KPZ universality was recently conjectured to also describe spin transport in the one-dimensional quantum Heisenberg model. We tested this conjecture by experimentally probing transport in a cold-atom quantum simulator via the relaxation of domain walls in spin chains of up to 50 spins. We found that domain-wall relaxation is indeed governed by the KPZ dynamical exponent z = 3/2 and that the occurrence of KPZ scaling requires both integrability and a nonabelian SU(2) symmetry. Finally, we leveraged the single-spin-sensitive detection enabled by the quantum gas microscope to measure an observable based on spin-transport statistics. Our results yield a clear signature of the nonlinearity that is a hallmark of KPZ universality.
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Affiliation(s)
- David Wei
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Antonio Rubio-Abadal
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Bingtian Ye
- Department of Physics, University of California, Berkeley, CA 94720, USA
| | - Francisco Machado
- Department of Physics, University of California, Berkeley, CA 94720, USA.,Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Jack Kemp
- Department of Physics, University of California, Berkeley, CA 94720, USA
| | - Kritsana Srakaew
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Simon Hollerith
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Jun Rui
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Sarang Gopalakrishnan
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA.,Department of Physics and Astronomy, College of Staten Island, Staten Island, NY 10314, USA
| | - Norman Y Yao
- Department of Physics, University of California, Berkeley, CA 94720, USA.,Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Immanuel Bloch
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany.,Fakultät für Physik, Ludwig-Maximilians-Universität, 80799 Munich, Germany
| | - Johannes Zeiher
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
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13
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Zawadzki K, Skelt AH, D'Amico I. Approximating quantum thermodynamic properties using DFT. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:274002. [PMID: 35405664 DOI: 10.1088/1361-648x/ac6648] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Accepted: 04/11/2022] [Indexed: 06/14/2023]
Abstract
The fabrication, utilisation, and efficiency of quantum technology devices rely on a good understanding of quantum thermodynamic properties. Many-body systems are often used as hardware for these quantum devices, but interactions between particles make the complexity of related calculations grow exponentially with the system size. Here we explore and systematically compare 'simple' and 'hybrid' approximations to the average work and entropy variation built on static density functional theory concepts. These approximations are computationally cheap and could be applied to large systems. We exemplify them considering driven one-dimensional Hubbard chains and show that, for 'simple' approximations and low to medium temperatures, it pays to consider a good estimate of the Kohn-Sham Hamiltonian to approximate the driving Hamiltonian. Our results confirm that a 'hybrid' approach, requiring a very good approximation of the initial and, for the entropy, final states of the system, provides great improvements. This approach should be particularly efficient when many-body effects are not increased by the driving Hamiltonian.
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Affiliation(s)
- K Zawadzki
- ICTP South American Institute for Fundamental Research, IFT-UNESP, São Paulo CEP: 01140-070, Brazil
| | - A H Skelt
- Department of Physics, University of York, York YO10 5DD, United Kingdom
| | - I D'Amico
- Department of Physics, University of York, York YO10 5DD, United Kingdom
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14
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Bhattacharya U, Grass T, Bachtold A, Lewenstein M, Pistolesi F. Phonon-Induced Pairing in Quantum Dot Quantum Simulator. NANO LETTERS 2021; 21:9661-9667. [PMID: 34757742 PMCID: PMC8631338 DOI: 10.1021/acs.nanolett.1c03457] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/06/2021] [Revised: 11/03/2021] [Indexed: 06/13/2023]
Abstract
Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well-studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context, we study the behavior of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the system presents a transition from the Mott insulating state to a polaronic state, with the appearance of pairing correlations and the breaking of the translational symmetry. These findings will motivate further theoretical and experimental efforts to employ nanoelectromechanical systems to simulate strongly correlated systems with electron-phonon interactions.
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Affiliation(s)
- Utso Bhattacharya
- ICFO-Institut
de Ciencies Fotoniques, The Barcelona Institute
of Science and Technology, Castelldefels, Barcelona 08860, Spain
- Max-Planck-Institut
für Quantenoptik, D-85748 Garching, Germany
| | - Tobias Grass
- ICFO-Institut
de Ciencies Fotoniques, The Barcelona Institute
of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Adrian Bachtold
- ICFO-Institut
de Ciencies Fotoniques, The Barcelona Institute
of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Maciej Lewenstein
- ICFO-Institut
de Ciencies Fotoniques, The Barcelona Institute
of Science and Technology, Castelldefels, Barcelona 08860, Spain
- ICREA, Pg. Lluis Companys
23, 08010 Barcelona, Spain
| | - Fabio Pistolesi
- Univ.
Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
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15
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Kokail C, Sundar B, Zache TV, Elben A, Vermersch B, Dalmonte M, van Bijnen R, Zoller P. Quantum Variational Learning of the Entanglement Hamiltonian. PHYSICAL REVIEW LETTERS 2021; 127:170501. [PMID: 34739272 DOI: 10.1103/physrevlett.127.170501] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Revised: 08/20/2021] [Accepted: 09/01/2021] [Indexed: 06/13/2023]
Abstract
Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. Optimal variational parameters are determined in a feedback loop, involving quench dynamics with the deformed Hamiltonian as a quantum processing step, and classical optimization. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions. Subsequent on-device spectroscopy enables a direct measurement of the entanglement spectrum, which we illustrate for a Fermi Hubbard model in a topological phase.
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Affiliation(s)
- Christian Kokail
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - Bhuvanesh Sundar
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- JILA, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Torsten V Zache
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - Andreas Elben
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Benoît Vermersch
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Univ. Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
| | - Marcello Dalmonte
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- SISSA, via Bonomea 265, 34136 Trieste, Italy
| | - Rick van Bijnen
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - Peter Zoller
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
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16
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Koepsell J, Bourgund D, Sompet P, Hirthe S, Bohrdt A, Wang Y, Grusdt F, Demler E, Salomon G, Gross C, Bloch I. Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid. Science 2021; 374:82-86. [PMID: 34591626 DOI: 10.1126/science.abe7165] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
[Figure: see text].
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Affiliation(s)
- Joannis Koepsell
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany
| | - Dominik Bourgund
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany
| | - Pimonpan Sompet
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany
| | - Sarah Hirthe
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany
| | - Annabelle Bohrdt
- Munich Center for Quantum Science and Technology, 80799 München, Germany.,Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - Yao Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Department of Physics and Astronomy, Clemson University, Clemson, SC 29631, USA
| | - Fabian Grusdt
- Munich Center for Quantum Science and Technology, 80799 München, Germany.,Fakultät für Physik, Ludwig-Maximilians-Universität, 80799 München, Germany
| | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Guillaume Salomon
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany.,Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany.,The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, 22761 Hamburg, Germany
| | - Christian Gross
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany.,Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
| | - Immanuel Bloch
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany.,Fakultät für Physik, Ludwig-Maximilians-Universität, 80799 München, Germany
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17
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Gluza M, Eisert J. Recovering Quantum Correlations in Optical Lattices from Interaction Quenches. PHYSICAL REVIEW LETTERS 2021; 127:090503. [PMID: 34506183 DOI: 10.1103/physrevlett.127.090503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Revised: 03/29/2021] [Accepted: 07/13/2021] [Indexed: 06/13/2023]
Abstract
Quantum simulations with ultracold atoms in optical lattices open up an exciting path toward understanding strongly interacting quantum systems. Atom gas microscopes are crucial for this as they offer single-site density resolution, unparalleled in other quantum many-body systems. However, currently a direct measurement of local coherent currents is out of reach. In this Letter, we show how to achieve that by measuring densities that are altered in response to quenches to noninteracting dynamics, e.g., after tilting the optical lattice. For this, we establish a data analysis method solving the closed set of equations relating tunneling currents and atom number dynamics, allowing us to reliably recover the full covariance matrix, including off-diagonal terms representing coherent currents. The signal processing builds upon semidefinite optimization, providing bona fide covariance matrices optimally matching the observed data. We demonstrate how the obtained information about noncommuting observables allows one to quantify entanglement at finite temperature, which opens up the possibility to study quantum correlations in quantum simulations going beyond classical capabilities.
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Affiliation(s)
- Marek Gluza
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - Jens Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
- Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany
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18
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Church MS, Rubenstein BM. Real-time dynamics of strongly correlated fermions using auxiliary field quantum Monte Carlo. J Chem Phys 2021; 154:184103. [PMID: 34241020 DOI: 10.1063/5.0049116] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Spurred by recent technological advances, there is a growing demand for computational methods that can accurately predict the dynamics of correlated electrons. Such methods can provide much-needed theoretical insights into the electron dynamics probed via time-resolved spectroscopy experiments and observed in non-equilibrium ultracold atom experiments. In this article, we develop and benchmark a numerically exact Auxiliary Field Quantum Monte Carlo (AFQMC) method for modeling the dynamics of correlated electrons in real time. AFQMC has become a powerful method for predicting the ground state and finite temperature properties of strongly correlated systems mostly by employing constraints to control the sign problem. Our initial goal in this work is to determine how well AFQMC generalizes to real-time electron dynamics problems without constraints. By modeling the repulsive Hubbard model on different lattices and with differing initial electronic configurations, we show that real-time AFQMC is capable of accurately capturing long-lived electronic coherences beyond the reach of mean field techniques. While the times to which we can meaningfully model decrease with increasing correlation strength and system size as a result of the exponential growth of the dynamical phase problem, we show that our technique can model the short-time behavior of strongly correlated systems to very high accuracy. Crucially, we find that importance sampling, combined with a novel adaptive active space sampling technique, can substantially lengthen the times to which we can simulate. These results establish real-time AFQMC as a viable technique for modeling the dynamics of correlated electron systems and serve as a basis for future sampling advances that will further mitigate the dynamical phase problem.
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Affiliation(s)
- Matthew S Church
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA
| | - Brenda M Rubenstein
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA
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19
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Lenihan C, Kim AJ, Šimkovic Iv F, Kozik E. Entropy in the Non-Fermi-Liquid Regime of the Doped 2D Hubbard Model. PHYSICAL REVIEW LETTERS 2021; 126:105701. [PMID: 33784123 DOI: 10.1103/physrevlett.126.105701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Accepted: 01/28/2021] [Indexed: 06/12/2023]
Abstract
We study thermodynamic properties of the doped Hubbard model on the square lattice in the regime of strong charge and spin fluctuations at low temperatures near the metal-to-insulator crossover and obtain results with controlled accuracy using the diagrammatic Monte Carlo method directly in the thermodynamic limit. The behavior of the entropy reveals a non-Fermi-liquid state at sufficiently high interactions near half filling: A maximum in the entropy at nonzero doping develops as the coupling strength is increased, along with an inflection point, evidencing a metal to non-Fermi-liquid crossover. The specific heat exhibits additional distinctive features of a non-Fermi-liquid state. Measurements of the entropy can, therefore, be used as a probe of the state of the system in quantum simulation experiments with ultracold atoms in optical lattices.
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Affiliation(s)
- Connor Lenihan
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - Aaram J Kim
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - Fedor Šimkovic Iv
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
- Centre de Physique Théorique, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau, France
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
| | - Evgeny Kozik
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
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20
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Grusdt F, Pollet L. Z_{2} Parton Phases in the Mixed-Dimensional t-J_{z} Model. PHYSICAL REVIEW LETTERS 2020; 125:256401. [PMID: 33416402 DOI: 10.1103/physrevlett.125.256401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2020] [Accepted: 11/19/2020] [Indexed: 06/12/2023]
Abstract
We study the interplay of spin and charge degrees of freedom in a doped Ising antiferromagnet, where the motion of charges is restricted to one dimension. The phase diagram of this mixed-dimensional t-J_{z} model can be understood in terms of spinless chargons coupled to a Z_{2} lattice gauge field. The antiferromagnetic couplings give rise to interactions between Z_{2} electric field lines which, in turn, lead to a robust stripe phase at low temperatures. At higher temperatures, a confined meson-gas phase is found for low doping whereas at higher doping values, a robust deconfined chargon-gas phase is seen, which features hidden antiferromagnetic order. We confirm these phases in quantum Monte Carlo simulations. Our model can be implemented and its phases detected with existing technology in ultracold atom experiments. The critical temperature for stripe formation with a sufficiently high hole concentration is around the spin-exchange energy J_{z}, i.e., well within reach of current experiments.
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Affiliation(s)
- Fabian Grusdt
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, München D-80333, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Lode Pollet
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, München D-80333, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
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21
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Spin transport in a tunable Heisenberg model realized with ultracold atoms. Nature 2020; 588:403-407. [DOI: 10.1038/s41586-020-3033-y] [Citation(s) in RCA: 82] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2020] [Accepted: 09/25/2020] [Indexed: 11/08/2022]
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22
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Bastianello A, De Luca A, Doyon B, De Nardis J. Thermalization of a Trapped One-Dimensional Bose Gas via Diffusion. PHYSICAL REVIEW LETTERS 2020; 125:240604. [PMID: 33412013 DOI: 10.1103/physrevlett.125.240604] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Accepted: 11/04/2020] [Indexed: 06/12/2023]
Abstract
For a decade the fate of a one-dimensional gas of interacting bosons in an external trapping potential remained mysterious. We here show that whenever the underlying integrability of the gas is broken by the presence of the external potential, the inevitable diffusive rearrangements between the quasiparticles, quantified by the diffusion constants of the gas, eventually lead the system to thermalize at late times. We show that the full thermalizing dynamics can be described by the generalized hydrodynamics with diffusion and force terms, and we compare these predictions to numerical simulations. Finally, we provide an explanation for the slow thermalization rates observed in numerical and experimental settings: the hydrodynamics of integrable models is characterized by a continuity of modes, which can have arbitrarily small diffusion coefficients. As a consequence, the approach to thermalization can display prethermal plateau and relaxation dynamics with long polynomial finite-time corrections.
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Affiliation(s)
- Alvise Bastianello
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Andrea De Luca
- Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, F-95302 Cergy-Pontoise, France
| | - Benjamin Doyon
- Department of Mathematics, King's College London, Strand WC2R 2LS, London, United Kingdom
| | - Jacopo De Nardis
- Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium
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23
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Abstract
It has been a long-sought goal of quantum simulation to find answers to outstanding questions in condensed-matter physics. A famous example is finding the ground state and the excitations of the two-dimensional (2D) Hubbard model with strong repulsion below half-filling. This system is a doped antiferromagnet and is of great interest because of its possible relation to high-[Formula: see text] superconductors. Theoretically, the fermion excitations of this model are believed to split up into holons and spinons, and a moving holon is believed to leave behind it a string of "wrong" spins that mismatch with the antiferromagnetic background. Here, we show that the properties of the ground-state wavefunction and the holon excitation of the 2D Hubbard model can be revealed in unprecedented detail by using the imaging and the interference technique in atomic physics. They allow one to reveal the Marshall sign of the doped antiferromagnet. The region of wrong Marshall sign indicates the location of the holon string.
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24
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Hartke T, Oreg B, Jia N, Zwierlein M. Doublon-Hole Correlations and Fluctuation Thermometry in a Fermi-Hubbard Gas. PHYSICAL REVIEW LETTERS 2020; 125:113601. [PMID: 32975995 DOI: 10.1103/physrevlett.125.113601] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 07/19/2020] [Accepted: 08/14/2020] [Indexed: 06/11/2023]
Abstract
We report on the single atom and single site-resolved detection of the total density in a cold atom realization of the 2D Fermi-Hubbard model. Fluorescence imaging of doublons is achieved by splitting each lattice site into a double well, thereby separating atom pairs. Full density readout yields a direct measurement of the equation of state, including direct thermometry via the fluctuation-dissipation theorem. Site-resolved density correlations reveal the Pauli hole at low filling, and strong doublon-hole correlations near half filling. These are shown to account for the difference between local and nonlocal density fluctuations in the Mott insulator. Our technique enables the study of atom-resolved charge transport in the Fermi-Hubbard model, the site-resolved observation of molecules, and the creation of bilayer Fermi-Hubbard systems.
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Affiliation(s)
- Thomas Hartke
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Botond Oreg
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ningyuan Jia
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Martin Zwierlein
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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25
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De Nardis J, Gopalakrishnan S, Ilievski E, Vasseur R. Superdiffusion from Emergent Classical Solitons in Quantum Spin Chains. PHYSICAL REVIEW LETTERS 2020; 125:070601. [PMID: 32857584 DOI: 10.1103/physrevlett.125.070601] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
Finite-temperature spin transport in the quantum Heisenberg spin chain is known to be superdiffusive, and has been conjectured to lie in the Kardar-Parisi-Zhang (KPZ) universality class. Using a kinetic theory of transport, we compute the KPZ coupling strength for the Heisenberg chain as a function of temperature, directly from microscopics; the results agree well with density-matrix renormalization group simulations. We establish a rigorous quantum-classical correspondence between the "giant quasiparticles" that govern superdiffusion and solitons in the classical continuous Landau-Lifshitz ferromagnet. We conclude that KPZ universality has the same origin in classical and quantum integrable isotropic magnets: a finite-temperature gas of low-energy classical solitons.
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Affiliation(s)
- Jacopo De Nardis
- Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium
| | - Sarang Gopalakrishnan
- Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York 10314; Physics Program and Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, New York 10016, USA
| | - Enej Ilievski
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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26
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Koepsell J, Hirthe S, Bourgund D, Sompet P, Vijayan J, Salomon G, Gross C, Bloch I. Robust Bilayer Charge Pumping for Spin- and Density-Resolved Quantum Gas Microscopy. PHYSICAL REVIEW LETTERS 2020; 125:010403. [PMID: 32678648 DOI: 10.1103/physrevlett.125.010403] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Accepted: 06/09/2020] [Indexed: 06/11/2023]
Abstract
Quantum gas microscopy has emerged as a powerful new way to probe quantum many-body systems at the microscopic level. However, layered or efficient spin-resolved readout methods have remained scarce as they impose strong demands on the specific atomic species and constrain the simulated lattice geometry and size. Here we present a novel high-fidelity bilayer readout, which can be used for full spin- and density-resolved quantum gas microscopy of two-dimensional systems with arbitrary geometry. Our technique makes use of an initial Stern-Gerlach splitting into adjacent layers of a highly stable vertical superlattice and subsequent charge pumping to separate the layers by 21 μm. This separation enables independent high-resolution images of each layer. We benchmark our method by spin- and density-resolving two-dimensional Fermi-Hubbard systems. Our technique furthermore enables the access to advanced entropy engineering schemes, spectroscopic methods, or the realization of tunable bilayer systems.
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Affiliation(s)
- Joannis Koepsell
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Sarah Hirthe
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Dominik Bourgund
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Pimonpan Sompet
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Jayadev Vijayan
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Guillaume Salomon
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Christian Gross
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
- Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
| | - Immanuel Bloch
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
- Fakultät für Physik, Ludwig-Maximilians-Universität, 80799 München, Germany
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27
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Kim AJ, Simkovic F, Kozik E. Spin and Charge Correlations across the Metal-to-Insulator Crossover in the Half-Filled 2D Hubbard Model. PHYSICAL REVIEW LETTERS 2020; 124:117602. [PMID: 32242729 DOI: 10.1103/physrevlett.124.117602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2019] [Revised: 11/12/2019] [Accepted: 02/06/2020] [Indexed: 06/11/2023]
Abstract
The 2D Hubbard model with nearest-neighbor hopping on the square lattice and an average of one electron per site is known to undergo an extended crossover from metallic to insulating behavior driven by proliferating antiferromagnetic correlations. We study signatures of this crossover in spin and charge correlation functions and present results obtained with controlled accuracy using the diagrammatic Monte Carlo approach in the range of parameters amenable to experimental verification with ultracold atoms in optical lattices. The qualitative changes in charge and spin correlations associated with the crossover are observed at well-separated temperature scales, which encase the intermediary regime of non-Fermi-liquid character, where local magnetic moments are formed and nonlocal fluctuations in both channels are essential.
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Affiliation(s)
- Aaram J Kim
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - Fedor Simkovic
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - Evgeny Kozik
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
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28
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Dehollain JP, Mukhopadhyay U, Michal VP, Wang Y, Wunsch B, Reichl C, Wegscheider W, Rudner MS, Demler E, Vandersypen LMK. Nagaoka ferromagnetism observed in a quantum dot plaquette. Nature 2020; 579:528-533. [PMID: 32123352 DOI: 10.1038/s41586-020-2051-0] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2019] [Accepted: 01/08/2020] [Indexed: 11/09/2022]
Abstract
Engineered, highly controllable quantum systems are promising simulators of emergent physics beyond the simulation capabilities of classical computers1. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been debated for decades2,3. Here we use a quantum simulator consisting of a four-electron-site square plaquette of quantum dots4 to demonstrate Nagaoka ferromagnetism5. This form of itinerant magnetism has been rigorously studied theoretically6-9 but has remained unattainable in experiments. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find that the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and we can induce a transition to the low-spin state by changing the plaquette topology to an open chain. This demonstration of Nagaoka ferromagnetism highlights that quantum simulators can be used to study physical phenomena that have not yet been observed in any experimental system. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems.
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Affiliation(s)
- J P Dehollain
- QuTech, TU Delft, Delft, The Netherlands.,Kavli Institute of Nanoscience, TU Delft, Delft, The Netherlands.,School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney, New South Wales, Australia
| | - U Mukhopadhyay
- QuTech, TU Delft, Delft, The Netherlands.,Kavli Institute of Nanoscience, TU Delft, Delft, The Netherlands
| | - V P Michal
- QuTech, TU Delft, Delft, The Netherlands.,Kavli Institute of Nanoscience, TU Delft, Delft, The Netherlands
| | - Y Wang
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - B Wunsch
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - C Reichl
- Solid State Physics Laboratory, ETH Zürich, Zürich, Switzerland
| | - W Wegscheider
- Solid State Physics Laboratory, ETH Zürich, Zürich, Switzerland
| | - M S Rudner
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark.,Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - E Demler
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - L M K Vandersypen
- QuTech, TU Delft, Delft, The Netherlands. .,Kavli Institute of Nanoscience, TU Delft, Delft, The Netherlands.
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29
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Šimkovic F, LeBlanc JPF, Kim AJ, Deng Y, Prokof'ev NV, Svistunov BV, Kozik E. Extended Crossover from a Fermi Liquid to a Quasiantiferromagnet in the Half-Filled 2D Hubbard Model. PHYSICAL REVIEW LETTERS 2020; 124:017003. [PMID: 31976700 DOI: 10.1103/physrevlett.124.017003] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2018] [Revised: 10/08/2019] [Indexed: 06/10/2023]
Abstract
The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover from Fermi liquid to insulating behavior in the parameter regime that precludes a metal-to-insulator transition. The intermediate crossover state is best described as a non-Fermi liquid with a partially gapped Fermi surface.
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Affiliation(s)
- Fedor Šimkovic
- Department of Physics, Kings College London, Strand, London WC2R 2LS, United Kingdom
| | - J P F LeBlanc
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, Newfoundland and Labrador A1B 3X7, Canada
| | - Aaram J Kim
- Department of Physics, Kings College London, Strand, London WC2R 2LS, United Kingdom
| | - Youjin Deng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - N V Prokof'ev
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
- National Research Center "Kurchatov Institute," 123182 Moscow, Russia
| | - B V Svistunov
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
- National Research Center "Kurchatov Institute," 123182 Moscow, Russia
- Wilczek Quantum Center, School of Physics and Astronomy and T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Evgeny Kozik
- Department of Physics, Kings College London, Strand, London WC2R 2LS, United Kingdom
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30
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Huang EW, Sheppard R, Moritz B, Devereaux TP. Strange metallicity in the doped Hubbard model. Science 2019; 366:987-990. [DOI: 10.1126/science.aau7063] [Citation(s) in RCA: 46] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2018] [Revised: 12/28/2018] [Accepted: 10/25/2019] [Indexed: 11/02/2022]
Abstract
Strange or bad metallic transport, defined by incompatibility with the conventional quasiparticle picture, is a theme common to many strongly correlated materials, including high-temperature superconductors. The Hubbard model represents a minimal starting point for modeling strongly correlated systems. Here we demonstrate strange metallic transport in the doped two-dimensional Hubbard model using determinantal quantum Monte Carlo calculations. Over a wide range of doping, we observe resistivities exceeding the Mott-Ioffe-Regel limit with linear temperature dependence. The temperatures of our calculations extend to as low as 1/40 of the noninteracting bandwidth, placing our findings in the degenerate regime relevant to experimental observations of strange metallicity. Our results provide a foundation for connecting theories of strange metals to models of strongly correlated materials.
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31
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Koepsell J, Vijayan J, Sompet P, Grusdt F, Hilker TA, Demler E, Salomon G, Bloch I, Gross C. Imaging magnetic polarons in the doped Fermi–Hubbard model. Nature 2019; 572:358-362. [DOI: 10.1038/s41586-019-1463-1] [Citation(s) in RCA: 72] [Impact Index Per Article: 14.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2018] [Accepted: 06/10/2019] [Indexed: 11/09/2022]
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32
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Bhattaram K, Khatami E. Lanczos-boosted numerical linked-cluster expansion for quantum lattice models. Phys Rev E 2019; 100:013305. [PMID: 31499902 DOI: 10.1103/physreve.100.013305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2018] [Indexed: 06/10/2023]
Abstract
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the limiting factor for these calculations. Here we show that a partial diagonalization of the largest clusters in the expansion using the Lanczos algorithm can be as useful as full diagonalization for the method while mitigating some of the time and memory issues. As test cases, we consider the frustrated Heisenberg model on the checkerboard lattice and the Fermi-Hubbard model on the square lattice. We find that our approach can surpass state of the art in performance in a parallel environment.
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Affiliation(s)
- Krishnakumar Bhattaram
- Lynbrook High School, 1280 Johnson Ave., San José, California 95129, USA
- Department of Physics and Astronomy, San José State University, San José, California 95192, USA
| | - Ehsan Khatami
- Department of Physics and Astronomy, San José State University, San José, California 95192, USA
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33
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Anderson R, Wang F, Xu P, Venu V, Trotzky S, Chevy F, Thywissen JH. Conductivity Spectrum of Ultracold Atoms in an Optical Lattice. PHYSICAL REVIEW LETTERS 2019; 122:153602. [PMID: 31050527 DOI: 10.1103/physrevlett.122.153602] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2018] [Indexed: 06/09/2023]
Abstract
We measure the conductivity of neutral fermions in a cubic optical lattice. Using in situ fluorescence microscopy, we observe the alternating current resultant from a single-frequency uniform force applied by displacement of a weak harmonic trapping potential. In the linear response regime, a neutral-particle analog of Ohm's law gives the conductivity as the ratio of total current to force. For various lattice depths, temperatures, interaction strengths, and fillings, we measure both real and imaginary conductivity, up to a frequency sufficient to capture the transport dynamics within the lowest band. The spectral width of the real conductivity reveals the current dissipation rate in the lattice, and the integrated spectral weight is related to thermodynamic properties of the system through a sum rule. The global conductivity decreases with increased band-averaged effective mass, which at high temperatures approaches a T-linear regime. Relaxation of current is observed to require a finite lattice depth, which breaks Galilean invariance and enables damping through collisions between fermions.
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Affiliation(s)
- Rhys Anderson
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Fudong Wang
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Peihang Xu
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Vijin Venu
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Stefan Trotzky
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Frédéric Chevy
- Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005 Paris, France
| | - Joseph H Thywissen
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1M1 Canada
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34
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Brantut JP. Transport with strong interactions. Science 2019; 363:344-345. [DOI: 10.1126/science.aaw1326] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Motion of spin and charge is explored with cold-atom quantum simulations
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35
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Nichols MA, Cheuk LW, Okan M, Hartke TR, Mendez E, Senthil T, Khatami E, Zhang H, Zwierlein MW. Spin transport in a Mott insulator of ultracold fermions. Science 2018; 363:383-387. [DOI: 10.1126/science.aat4387] [Citation(s) in RCA: 80] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2018] [Accepted: 11/20/2018] [Indexed: 11/02/2022]
Abstract
Strongly correlated materials are expected to feature unconventional transport properties, such that charge, spin, and heat conduction are potentially independent probes of the dynamics. In contrast to charge transport, the measurement of spin transport in such materials is highly challenging. We observed spin conduction and diffusion in a system of ultracold fermionic atoms that realizes the half-filled Fermi-Hubbard model. For strong interactions, spin diffusion is driven by super-exchange and doublon-hole–assisted tunneling, and strongly violates the quantum limit of charge diffusion. The technique developed in this work can be extended to finite doping, which can shed light on the complex interplay between spin and charge in the Hubbard model.
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