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Bohrdt A, Demler E, Grusdt F. Rotational Resonances and Regge-like Trajectories in Lightly Doped Antiferromagnets. PHYSICAL REVIEW LETTERS 2021; 127:197004. [PMID: 34797143 DOI: 10.1103/physrevlett.127.197004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 10/13/2021] [Indexed: 06/13/2023]
Abstract
Understanding the nature of charge carriers in doped Mott insulators holds the key to unravelling puzzling properties of strongly correlated electron systems, including cuprate superconductors. Several theoretical models suggested that dopants can be understood as bound states of partons, the analogues of quarks in high-energy physics. However, direct signatures of spinon-chargon bound states are lacking, both in experiment and theory. Here we propose a rotational variant of angle-resolved photo-emission spectroscopy (ARPES) and calculate rotational spectra numerically using the density-matrix renormalization group. We identify long-lived rotational resonances for an individual dopant, which we interpret as a direct indicator of the microscopic structure of spinon-chargon bound states. Similar to Regge trajectories reflecting the quark structure of mesons, we establish a linear dependence of the rotational energy on the superexchange coupling. The rotational peaks we find are strongly suppressed in standard ARPES spectra, but we suggest a multiphoton extension of ARPES which allows us to access rotational spectra. Our findings suggest that multiphoton spectroscopy experiments should provide new insights into emergent universal features of strongly correlated electron systems.
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Affiliation(s)
- A Bohrdt
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - E Demler
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - F Grusdt
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, München D-80333, Germany
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2
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Jiang YF, Yao H, Yang F. Possible Superconductivity with a Bogoliubov Fermi Surface in a Lightly Doped Kagome U(1) Spin Liquid. PHYSICAL REVIEW LETTERS 2021; 127:187003. [PMID: 34767423 DOI: 10.1103/physrevlett.127.187003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2020] [Revised: 05/22/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
Whether the doped t-J model on the Kagome lattice supports exotic superconductivity has not been decisively answered. In this Letter, we propose a new class of variational states for this model and perform a large-scale variational Monte Carlo simulation on it. The proposed variational states are parameterized by the SU(2)-gauge rotation angles, as the SU(2)-gauge structure hidden in the Gutzwiller-projected mean-field Ansatz for the undoped model is broken upon doping. These variational doped states smoothly connect to the previously studied U(1) π-flux or 0-flux states, and energy minimization among them yields a chiral noncentrosymmetric nematic superconducting state with 2×2-enlarged unit cell. Moreover, this pair density wave state possesses a finite Fermi surface for the Bogoliubov quasiparticles. We further study experimentally relevant properties of this intriguing pairing state.
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Affiliation(s)
- Yi-Fan Jiang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA
| | - Hong Yao
- Institute of Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Fan Yang
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
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3
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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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4
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Chiu CS, Ji G, Bohrdt A, Xu M, Knap M, Demler E, Grusdt F, Greiner M, Greif D. String patterns in the doped Hubbard model. Science 2020; 365:251-256. [PMID: 31320533 DOI: 10.1126/science.aav3587] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2018] [Accepted: 06/05/2019] [Indexed: 11/02/2022]
Abstract
Understanding strongly correlated quantum many-body states is one of the most difficult challenges in modern physics. For example, there remain fundamental open questions on the phase diagram of the Hubbard model, which describes strongly correlated electrons in solids. In this work, we realize the Hubbard Hamiltonian and search for specific patterns within the individual images of many realizations of strongly correlated ultracold fermions in an optical lattice. Upon doping a cold-atom antiferromagnet, we find consistency with geometric strings, entities that may explain the relationship between hole motion and spin order, in both pattern-based and conventional observables. Our results demonstrate the potential for pattern recognition to provide key insights into cold-atom quantum many-body systems.
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Affiliation(s)
- Christie S Chiu
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Geoffrey Ji
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Annabelle Bohrdt
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.,Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA.,Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Muqing Xu
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Michael Knap
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Eugene Demler
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Fabian Grusdt
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA.,Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Markus Greiner
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA.
| | - Daniel Greif
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
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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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Sachdev S. Topological order, emergent gauge fields, and Fermi surface reconstruction. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:014001. [PMID: 30210062 DOI: 10.1088/1361-6633/aae110] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This review describes how topological order associated with the presence of emergent gauge fields can reconstruct Fermi surfaces of metals, even in the absence of translational symmetry breaking. We begin with an introduction to topological order using Wegner's quantum [Formula: see text] gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying [Formula: see text] magnetic flux. The interplay between topological order and the breaking of global symmetry is described by the non-zero temperature statistical mechanics of classical XY models in dimension D = 3; such models also describe the zero temperature quantum phases of bosons with short-range interactions on the square lattice at integer filling. The topological state is again characterized by the expulsion of certain defects, in a state with fluctuating symmetry-breaking order, along with the presence of emergent gauge fields. The phase diagrams of the [Formula: see text] gauge theory and the XY models are obtained by embedding them in U(1) gauge theories, and by studying their Higgs and confining phases. These ideas are then applied to the single-band Hubbard model on the square lattice. A SU(2) gauge theory describes the fluctuations of spin-density-wave order, and its phase diagram is presented by analogy to the XY models. We obtain a class of zero temperature metallic states with fluctuating spin-density wave order, topological order associated with defect expulsion, deconfined emergent gauge fields, reconstructed Fermi surfaces (with 'chargon' or electron-like quasiparticles), but no broken symmetry. We conclude with the application of such metallic states to the pseudogap phase of the cuprates, and note the recent comparison with numerical studies of the Hubbard model and photoemission observations of the electron-doped cuprates. In a detour, we also discuss the influence of Berry phases, and how they can lead to deconfined quantum critical points: this applies to bosons on the square lattice at half-integer filling, and to quantum dimer models.
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Affiliation(s)
- Subir Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, United States of America. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada. Department of Physics, Stanford University, Stanford, CA 94305, United States of America
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Feldmeier J, Huber S, Punk M. Exact Solution of a Two-Species Quantum Dimer Model for Pseudogap Metals. PHYSICAL REVIEW LETTERS 2018; 120:187001. [PMID: 29775366 DOI: 10.1103/physrevlett.120.187001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2017] [Indexed: 06/08/2023]
Abstract
We present an exact ground state solution of a quantum dimer model introduced by Punk, Allais, and Sachdev [Quantum dimer model for the pseudogap metal, Proc. Natl. Acad. Sci. U.S.A. 112, 9552 (2015).PNASA60027-842410.1073/pnas.1512206112], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-T_{c} cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.
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Affiliation(s)
- Johannes Feldmeier
- Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-University Munich, 80333 Munich, Germany
| | - Sebastian Huber
- Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-University Munich, 80333 Munich, Germany
| | - Matthias Punk
- Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-University Munich, 80333 Munich, Germany
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Abstract
We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.
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Jiang HC, Devereaux T, Kivelson SA. Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid. PHYSICAL REVIEW LETTERS 2017; 119:067002. [PMID: 28949592 DOI: 10.1103/physrevlett.119.067002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2017] [Indexed: 06/07/2023]
Abstract
We address the problem of a lightly doped spin liquid through a large-scale density-matrix renormalization group study of the t-J model on a kagome lattice with a small but nonzero concentration δ of doped holes. It is now widely accepted that the undoped (δ=0) spin-1/2 Heisenberg antiferromagnet has a spin-liquid ground state. Theoretical arguments have been presented that light doping of such a spin liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal. Instead, we infer that the doped holes form an insulating charge-density wave state with one doped hole per unit cell, i.e., a Wigner crystal. Spin correlations remain short ranged, as in the spin-liquid parent state, from which we infer that the state is a crystal of spinless holons, rather than of holes. Our results may be relevant to kagome lattice herbertsmithite upon doping.
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Affiliation(s)
- Hong-Chen Jiang
- Stanford Institute for Materials and Energy Sciences, SLAC and Stanford University, Menlo Park, California 94025, USA
| | - T Devereaux
- Stanford Institute for Materials and Energy Sciences, SLAC and Stanford University, Menlo Park, California 94025, USA
| | - S A Kivelson
- Department of Physics, Stanford University, Stanford, California 94305, USA
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10
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Sachdev S. Emergent gauge fields and the high-temperature superconductors. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2016; 374:rsta.2015.0248. [PMID: 27458260 DOI: 10.1098/rsta.2015.0248] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/17/2016] [Indexed: 06/06/2023]
Abstract
The quantum entanglement of many states of matter can be represented by electric and magnetic fields, much like those found in Maxwell's theory. These fields 'emerge' from the quantum structure of the many-electron state, rather than being fundamental degrees of freedom of the vacuum. I review basic aspects of the theory of emergent gauge fields in insulators in an intuitive manner. In metals, Fermi liquid (FL) theory relies on adiabatic continuity from the free electron state, and its central consequence is the existence of long-lived electron-like quasi-particles around a Fermi surface enclosing a volume determined by the total density of electrons, via the Luttinger theorem. However, long-range entanglement and emergent gauge fields can also be present in metals. I focus on the 'fractionalized Fermi liquid' (FL*) state, which also has long-lived electron-like quasi-particles around a Fermi surface; however, the Luttinger theorem on the Fermi volume is violated, and this requires the presence of emergent gauge fields, and the associated loss of adiabatic continuity with the free electron state. Finally, I present a brief survey of some recent experiments in the hole-doped cuprate superconductors, and interpret the properties of the pseudogap regime in the framework of the FL* theory.This article is part of the themed issue 'Unifying physics and technology in light of Maxwell's equations'.
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Affiliation(s)
- Subir Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
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Single reconstructed Fermi surface pocket in an underdoped single-layer cuprate superconductor. Nat Commun 2016; 7:12244. [PMID: 27448102 PMCID: PMC4961849 DOI: 10.1038/ncomms12244] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2015] [Accepted: 06/15/2016] [Indexed: 12/01/2022] Open
Abstract
The observation of a reconstructed Fermi surface via quantum oscillations in hole-doped cuprates opened a path towards identifying broken symmetry states in the pseudogap regime. However, such an identification has remained inconclusive due to the multi-frequency quantum oscillation spectra and complications accounting for bilayer effects in most studies. We overcome these impediments with high-resolution measurements on the structurally simpler cuprate HgBa2CuO4+δ (Hg1201), which features one CuO2 plane per primitive unit cell. We find only a single oscillatory component with no signatures of magnetic breakdown tunnelling to additional orbits. Therefore, the Fermi surface comprises a single quasi-two-dimensional pocket. Quantitative modelling of these results indicates that a biaxial charge density wave within each CuO2 plane is responsible for the reconstruction and rules out criss-crossed charge stripes between layers as a viable alternative in Hg1201. Lastly, we determine that the characteristic gap between reconstructed pockets is a significant fraction of the pseudogap energy. The identification of broken symmetry states in underdoped cuprate superconductors via quantum oscillation measurements remains inconclusive. Here, Chan et al. report the reconstructed Fermi surface of HgBa2CuO4+δ comprises only a single pocket indicating a biaxial charge-density-wave order within each CuO2 plane.
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