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Defenu N, Mukamel D, Ruffo S. Ensemble Inequivalence in Long-Range Quantum Systems. PHYSICAL REVIEW LETTERS 2024; 133:050403. [PMID: 39159084 DOI: 10.1103/physrevlett.133.050403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2024] [Accepted: 06/26/2024] [Indexed: 08/21/2024]
Abstract
Ensemble inequivalence, i.e., the possibility of observing different thermodynamic properties depending on the statistical ensemble which describes the system, is one of the hallmarks of long-range physics, which has been demonstrated in numerous classical systems. Here, an example of ensemble inequivalence of a long-range quantum ferromagnet is presented. While the T=0 microcanonical quantum phase-diagram coincides with that of the canonical ensemble, the phase diagrams of the two ensembles are different at finite temperature. This is in contrast with the common lore of statistical mechanics of systems with short-range interactions where thermodynamic properties are bound to coincide for macroscopic systems described by different ensembles. The consequences of these findings in the context of atomic, molecular, and optical setups are delineated.
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2
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Feng L, Katz O, Haack C, Maghrebi M, Gorshkov AV, Gong Z, Cetina M, Monroe C. Continuous symmetry breaking in a trapped-ion spin chain. Nature 2023; 623:713-717. [PMID: 37968402 DOI: 10.1038/s41586-023-06656-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Accepted: 09/20/2023] [Indexed: 11/17/2023]
Abstract
One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions1. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter2,3. Our preparation relies on simultaneous control over an array of tightly focused individual addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.
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Affiliation(s)
- Lei Feng
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
| | - Or Katz
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
| | - Casey Haack
- Department of Physics, Colorado School of Mines, Golden, CO, USA
| | - Mohammad Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansings, MI, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland and NIST, College Park, MD, USA
| | - Zhexuan Gong
- Department of Physics, Colorado School of Mines, Golden, CO, USA
| | - Marko Cetina
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA
| | - Christopher Monroe
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
- IonQ, Inc., College Park, MD, USA.
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3
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Su L, Douglas A, Szurek M, Groth R, Ozturk SF, Krahn A, Hébert AH, Phelps GA, Ebadi S, Dickerson S, Ferlaino F, Marković O, Greiner M. Dipolar quantum solids emerging in a Hubbard quantum simulator. Nature 2023; 622:724-729. [PMID: 37880438 DOI: 10.1038/s41586-023-06614-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Accepted: 09/05/2023] [Indexed: 10/27/2023]
Abstract
In quantum mechanical many-body systems, long-range and anisotropic interactions promote rich spatial structure and can lead to quantum frustration, giving rise to a wealth of complex, strongly correlated quantum phases1. Long-range interactions play an important role in nature; however, quantum simulations of lattice systems have largely not been able to realize such interactions. A wide range of efforts are underway to explore long-range interacting lattice systems using polar molecules2-5, Rydberg atoms2,6-8, optical cavities9-11 or magnetic atoms12-15. Here we realize novel quantum phases in a strongly correlated lattice system with long-range dipolar interactions using ultracold magnetic erbium atoms. As we tune the dipolar interaction to be the dominant energy scale in our system, we observe quantum phase transitions from a superfluid into dipolar quantum solids, which we directly detect using quantum gas microscopy with accordion lattices. Controlling the interaction anisotropy by orienting the dipoles enables us to realize a variety of stripe-ordered states. Furthermore, by transitioning non-adiabatically through the strongly correlated regime, we observe the emergence of a range of metastable stripe-ordered states. This work demonstrates that novel strongly correlated quantum phases can be realized using long-range dipolar interactions in optical lattices, opening the door to quantum simulations of a wide range of lattice models with long-range and anisotropic interactions.
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Affiliation(s)
- Lin Su
- Department of Physics, Harvard University, Cambridge, MA, USA.
| | | | - Michal Szurek
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Robin Groth
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - S Furkan Ozturk
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Aaron Krahn
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Anne H Hébert
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Francesca Ferlaino
- Institut für Experimentalphysik, Universität Innsbruck, Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Innsbruck, Austria
| | - Ognjen Marković
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA.
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Andreucci F, Lepri S, Ruffo S, Trombettoni A. Nonequilibrium steady states of long-range coupled harmonic chains. Phys Rev E 2023; 108:024115. [PMID: 37723711 DOI: 10.1103/physreve.108.024115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 07/12/2023] [Indexed: 09/20/2023]
Abstract
We perform a numerical study of transport properties of a one-dimensional chain with couplings decaying as an inverse power r^{-(1+σ)} of the intersite distance r and open boundary conditions, interacting with two heat reservoirs. Despite its simplicity, the model displays highly nontrivial features in the strong long-range regime -1<σ<0. At weak coupling with the reservoirs, the energy flux departs from the predictions of perturbative theory and displays anomalous superdiffusive scaling of the heat current with the chain size. We trace this behavior back to the transmission spectrum of the chain, which displays a self-similar structure with a characteristic σ-dependent fractal dimension.
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Affiliation(s)
| | - Stefano Lepri
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy
| | - Stefano Ruffo
- SISSA and INFN, Sezione di Trieste, Via Bonomea 265, 34136 Trieste, Italy
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy
| | - Andrea Trombettoni
- SISSA and INFN, Sezione di Trieste, Via Bonomea 265, 34136 Trieste, Italy
- Department of Physics, University of Trieste, Strada Costiera 11, 34151 Trieste, Italy
- DEMOCRITOS Simulation Center, IOM, CNR, Via Bonomea 265, 34136 Trieste, Italy
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5
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Giachetti G, Defenu N. Entanglement propagation and dynamics in non-additive quantum systems. Sci Rep 2023; 13:12388. [PMID: 37524738 PMCID: PMC10390585 DOI: 10.1038/s41598-023-37984-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 06/30/2023] [Indexed: 08/02/2023] Open
Abstract
The prominent collective character of long-range interacting quantum systems makes them promising candidates for quantum technological applications. Yet, lack of additivity overthrows the traditional picture for entanglement scaling and transport, due to the breakdown of the common mechanism based on excitations propagation and confinement. Here, we describe the dynamics of the entanglement entropy in many-body quantum systems with a diverging contribution to the internal energy from the long-range two body potential. While in the strict thermodynamic limit entanglement dynamics is shown to be suppressed, a rich mosaic of novel scaling regimes is observed at intermediate system sizes, due to the possibility to trigger multiple resonant modes in the global dynamics. Quantitative predictions on the shape and timescales of entanglement propagation are made, paving the way to the observation of these phases in current quantum simulators. This picture is connected and contrasted with the case of local many body systems subject to Floquet driving.
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Affiliation(s)
- Guido Giachetti
- SISSA and INFN Sezione di Trieste, Via Bonomea 265, 34136, Trieste, Italy
| | - Nicolò Defenu
- Institut für Theoretische Physik, ETH Zürich, Wolfgang-Pauli-Str. 27, Zurich, Switzerland.
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Balducci F, Gambassi A, Lerose A, Scardicchio A, Vanoni C. Localization and Melting of Interfaces in the Two-Dimensional Quantum Ising Model. PHYSICAL REVIEW LETTERS 2022; 129:120601. [PMID: 36179178 DOI: 10.1103/physrevlett.129.120601] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Revised: 06/10/2022] [Accepted: 08/04/2022] [Indexed: 06/16/2023]
Abstract
We study the nonequilibrium evolution of coexisting ferromagnetic domains in the two-dimensional quantum Ising model-a setup relevant in several contexts, from quantum nucleation dynamics and false-vacuum decay scenarios to recent experiments with Rydberg-atom arrays. We demonstrate that the quantum-fluctuating interface delimiting a large bubble can be studied as an effective one-dimensional system through a "holographic" mapping. For the considered model, the emergent interface excitations map to an integrable chain of fermionic particles. We discuss how this integrability is broken by geometric features of the bubbles and by corrections in inverse powers of the ferromagnetic coupling, and provide a lower bound to the timescale after which the bubble is ultimately expected to melt. Remarkably, we demonstrate that a symmetry-breaking longitudinal field gives rise to a robust ergodicity breaking in two dimensions, a phenomenon underpinned by Stark many-body localization of the emergent fermionic excitations of the interface.
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Affiliation(s)
- Federico Balducci
- SISSA-International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy
- INFN Sezione di Trieste-Via Valerio 2, 34127 Trieste, Italy
- The Abdus Salam ICTP-Strada Costiera 11, 34151 Trieste, Italy
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy
- INFN Sezione di Trieste-Via Valerio 2, 34127 Trieste, Italy
| | - Alessio Lerose
- Department of Theoretical Physics, University of Geneva-Quai Ernest-Ansermet 30, 1205 Geneva, Switzerland
| | - Antonello Scardicchio
- INFN Sezione di Trieste-Via Valerio 2, 34127 Trieste, Italy
- The Abdus Salam ICTP-Strada Costiera 11, 34151 Trieste, Italy
| | - Carlo Vanoni
- SISSA-International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy
- INFN Sezione di Trieste-Via Valerio 2, 34127 Trieste, Italy
- The Abdus Salam ICTP-Strada Costiera 11, 34151 Trieste, Italy
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Sugimoto S, Hamazaki R, Ueda M. Eigenstate Thermalization in Long-Range Interacting Systems. PHYSICAL REVIEW LETTERS 2022; 129:030602. [PMID: 35905337 DOI: 10.1103/physrevlett.129.030602] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Revised: 03/27/2022] [Accepted: 06/16/2022] [Indexed: 05/16/2023]
Abstract
Motivated by recent ion experiments on tunable long-range interacting quantum systems [Neyenhuis et al., Sci. Adv. 3, e1700672 (2017)SACDAF2375-254810.1126/sciadv.1700672], we test the strong eigenstate thermalization hypothesis for systems with power-law interactions ∼1/r^{α}. We numerically demonstrate that the strong eigenstate thermalization hypothesis typically holds, at least for systems with α≥0.6, which include Coulomb, monopole-dipole, and dipole-dipole interactions. Compared with short-range interacting systems, the eigenstate expectation value of a generic local observable is shown to deviate significantly from its microcanonical ensemble average for long-range interacting systems. We find that Srednicki's ansatz breaks down for α≲1.0, at least for relatively large system sizes.
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Affiliation(s)
- Shoki Sugimoto
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Ryusuke Hamazaki
- Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR), RIKEN iTHEMS, Wako, Saitama 351-0198, Japan
| | - Masahito Ueda
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
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Wang J, Li AC. Dynamic crossover towards energy equipartition in the Fermi-Pasta-Ulam-Tsingou β model with long-range interactions. Phys Rev E 2022; 106:014135. [PMID: 35974610 DOI: 10.1103/physreve.106.014135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
Energy equipartition can be established in short-range systems after the dynamic process of thermalization. However, energy distribution between different degrees of freedom in systems with long-range interactions is unclear. We study the dynamics of energy relaxation in the Fermi-Pasta-Ulam-Tsingou β model with long-range quartic interactions, which decay as 1/d^{δ} with d being the lattice distance. The dynamic crossover of a mode-energy distribution from localized to equipartitioned with the increase of the power δ is observed. A transition of mode-energy distribution is identified around the value of δ=1, which usually serves as the distinction between strong and weak long-range couplings. We elucidate that the varying frequency overlapping of the mode-energy power spectrum is responsible for this dynamic crossover. Through further calculation of the spectral entropy, the minimum duration of quasistationary states, τ_{QSS}, is found at δ=2, which may provide possible dynamic explanations for the peculiar behavior of heat transport in long-range lattice chains. In addition, the double scaling in τ_{QSS} as a function of energy density is also observed in our long-range lattices. Our results not only contribute to understanding the dynamics of energy relaxation in long-range systems, but also shed light on the longstanding problem of thermalization and low-dimensional heat transport in short-range systems.
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Affiliation(s)
- Jian Wang
- College of Physical Science and Technology, Yangzhou University, Yangzhou 225002, People's Republic of China
| | - Ai-Chen Li
- College of Physical Science and Technology, Yangzhou University, Yangzhou 225002, People's Republic of China
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