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Title: Signatures of rare states and thermalization in a theory with confinement

Abstract

There is a dichotomy in the nonequilibrium dynamics of quantum many-body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains extensive memory about the initial state of the system. On the other hand, in generic systems such expectation values relax to stationary values described by the thermal ensemble, fixed solely by the energy of the state. At the heart of understanding, this dichotomy is the eigenstate thermalization hypothesis (ETH): individual eigenstates in nonintegrable systems are thermal, in the sense that expectation values agree with the thermal prediction at a temperature set by the energy of the eigenstate. In systems where ETH is violated, thermalization can be avoided. Thus, establishing the range of validity of ETH is crucial in understanding whether a given quantum system thermalizes. Here, we study a simple model with confinement, the quantum Ising chain with a longitudinal field, in which ETH is violated. Despite an absence of integrability, there exist rare (nonthermal) states that persist far into the spectrum. These arise as a direct consequence of confinement: pairs of particles are confined, forming new “meson” excitations whose energy can be extensive in the systemmore » size. We show that such states are nonthermal in both the continuum and in the low-energy spectrum of the corresponding lattice model. Here, we highlight that the presence of such states within the spectrum has important consequences, with certain quenches leading to an absence of thermalization and local observables evolving anomalously.« less

Authors:
 [1];  [2]; ORCiD logo [3]
  1. Univ. of Amsterdam, Amsterdam (The Netherlands)
  2. The Open Univ., Milton Keynes (United Kingdom); Univ. College London, London (United Kingdom)
  3. Brookhaven National Lab. (BNL), Upton, NY (United States)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1529074
Alternate Identifier(s):
OSTI ID: 1510834
Report Number(s):
BNL-211781-2019-JAAM
Journal ID: ISSN 2469-9950; PRBMDO
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 99; Journal Issue: 19; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Robinson, Neil J., James, Andrew J. A., and Konik, Robert M. Signatures of rare states and thermalization in a theory with confinement. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.99.195108.
Robinson, Neil J., James, Andrew J. A., & Konik, Robert M. Signatures of rare states and thermalization in a theory with confinement. United States. doi:10.1103/PhysRevB.99.195108.
Robinson, Neil J., James, Andrew J. A., and Konik, Robert M. Mon . "Signatures of rare states and thermalization in a theory with confinement". United States. doi:10.1103/PhysRevB.99.195108.
@article{osti_1529074,
title = {Signatures of rare states and thermalization in a theory with confinement},
author = {Robinson, Neil J. and James, Andrew J. A. and Konik, Robert M.},
abstractNote = {There is a dichotomy in the nonequilibrium dynamics of quantum many-body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains extensive memory about the initial state of the system. On the other hand, in generic systems such expectation values relax to stationary values described by the thermal ensemble, fixed solely by the energy of the state. At the heart of understanding, this dichotomy is the eigenstate thermalization hypothesis (ETH): individual eigenstates in nonintegrable systems are thermal, in the sense that expectation values agree with the thermal prediction at a temperature set by the energy of the eigenstate. In systems where ETH is violated, thermalization can be avoided. Thus, establishing the range of validity of ETH is crucial in understanding whether a given quantum system thermalizes. Here, we study a simple model with confinement, the quantum Ising chain with a longitudinal field, in which ETH is violated. Despite an absence of integrability, there exist rare (nonthermal) states that persist far into the spectrum. These arise as a direct consequence of confinement: pairs of particles are confined, forming new “meson” excitations whose energy can be extensive in the system size. We show that such states are nonthermal in both the continuum and in the low-energy spectrum of the corresponding lattice model. Here, we highlight that the presence of such states within the spectrum has important consequences, with certain quenches leading to an absence of thermalization and local observables evolving anomalously.},
doi = {10.1103/PhysRevB.99.195108},
journal = {Physical Review B},
number = 19,
volume = 99,
place = {United States},
year = {2019},
month = {5}
}

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Works referenced in this record:

Colloquium : Nonequilibrium dynamics of closed interacting quantum systems
journal, August 2011

  • Polkovnikov, Anatoli; Sengupta, Krishnendu; Silva, Alessandro
  • Reviews of Modern Physics, Vol. 83, Issue 3
  • DOI: 10.1103/RevModPhys.83.863

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
journal, April 2016


From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
journal, May 2016


Quench dynamics and relaxation in isolated integrable quantum spin chains
journal, June 2016


Quantum quenches in 1  +  1 dimensional conformal field theories
journal, June 2016


Quantum quenches in the Luttinger model and its close relatives
journal, June 2016


Conformal field theory out of equilibrium: a review
journal, June 2016


The Quench Action
journal, June 2016


Generalized Gibbs ensemble in integrable lattice models
journal, June 2016


Prethermalization and universal dynamics in near-integrable quantum systems
journal, June 2016

  • Langen, Tim; Gasenzer, Thomas; Schmiedmayer, Jörg
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6
  • DOI: 10.1088/1742-5468/2016/06/064009

Quasilocal charges in integrable lattice systems
journal, June 2016

  • Ilievski, Enej; Medenjak, Marko; Prosen, Tomaž
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6
  • DOI: 10.1088/1742-5468/2016/06/064008

Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
journal, June 2016


Equilibration properties of classical integrable field theories
journal, June 2016


A quantum Newton's cradle
journal, April 2006

  • Kinoshita, Toshiya; Wenger, Trevor; Weiss, David S.
  • Nature, Vol. 440, Issue 7086
  • DOI: 10.1038/nature04693

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
journal, March 2007

  • Lewenstein, Maciej; Sanpera, Anna; Ahufinger, Veronica
  • Advances in Physics, Vol. 56, Issue 2
  • DOI: 10.1080/00018730701223200

Quantum statistical mechanics in a closed system
journal, February 1991


Chaos and quantum thermalization
journal, August 1994


Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008

  • Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim
  • Nature, Vol. 452, Issue 7189
  • DOI: 10.1038/nature06838

Breakdown of Thermalization in Finite One-Dimensional Systems
journal, September 2009


Alternatives to Eigenstate Thermalization
journal, March 2012


Eigenstate thermalization: Deutsch’s approach and beyond
journal, May 2015


Eigenstate thermalization hypothesis
journal, July 2018


Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
journal, December 2010


Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
journal, September 2010


Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
journal, March 2010


Real-time dynamics of typical and untypical states in nonintegrable systems
journal, May 2018


Finite-size scaling analysis of the eigenstate thermalization hypothesis in a one-dimensional interacting Bose gas
journal, January 2013


Eigenstate thermalization hypothesis and integrability in quantum spin chains
journal, April 2015


Finite-size scaling of eigenstate thermalization
journal, April 2014


Relevance of the eigenstate thermalization hypothesis for thermal relaxation
journal, January 2015


Eigenstate thermalization in the two-dimensional transverse field Ising model
journal, March 2016


Eigenstate thermalization hypothesis in quantum dimer models
journal, September 2017


Testing whether all eigenstates obey the eigenstate thermalization hypothesis
journal, November 2014


Exact excited states of nonintegrable models
journal, December 2018


Probing many-body dynamics on a 51-atom quantum simulator
journal, November 2017

  • Bernien, Hannes; Schwartz, Sylvain; Keesling, Alexander
  • Nature, Vol. 551, Issue 7682
  • DOI: 10.1038/nature24622

Weak ergodicity breaking from quantum many-body scars
journal, May 2018


Signatures of integrability in the dynamics of Rydberg-blockaded chains
journal, April 2019


Periodic Orbits, Entanglement, and Quantum Many-Body Scars in Constrained Models: Matrix Product State Approach
journal, January 2019


Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations
journal, October 2018


Cold Atoms Bear a Quantum Scar
journal, October 2018


Thermalization of a Strongly Interacting Closed Spin System: From Coherent Many-Body Dynamics to a Fokker-Planck Equation
journal, March 2012


Equilibration of quantum hard rods in one dimension
journal, February 2013


Dynamics of many-body localization in a translation-invariant quantum glass model
journal, September 2015


Quantum Slow Relaxation and Metastability due to Dynamical Constraints
journal, July 2018


Confined Quasiparticle Dynamics in Long-Range Interacting Quantum Spin Chains
journal, April 2019


Quasilocalized excitations induced by long-range interactions in translationally invariant quantum spin chains
journal, March 2019


Pushing the Limits of the Eigenstate Thermalization Hypothesis towards Mesoscopic Quantum Systems
journal, April 2014


Quench Dynamics and Nonequilibrium Phase Diagram of the Bose-Hubbard Model
journal, April 2007


Strongly Correlated Fermions after a Quantum Quench
journal, May 2007


Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas
journal, February 2012

  • Trotzky, S.; Chen, Y-A.; Flesch, A.
  • Nature Physics, Vol. 8, Issue 4
  • DOI: 10.1038/nphys2232

Quantum quenches in two spatial dimensions using chain array matrix product states
journal, October 2015


Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods
journal, February 2018

  • James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe
  • Reports on Progress in Physics, Vol. 81, Issue 4
  • DOI: 10.1088/1361-6633/aa91ea

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases
journal, December 2015


Interaction Quench in the Hubbard Model
journal, May 2008


Real-time evolution for weak interaction quenches in quantum systems
journal, October 2009


New theoretical approaches for correlated systems in nonequilibrium
journal, December 2009

  • Eckstein, M.; Hackl, A.; Kehrein, S.
  • The European Physical Journal Special Topics, Vol. 180, Issue 1
  • DOI: 10.1140/epjst/e2010-01219-x

Quench dynamics in a model with tuneable integrability breaking
journal, April 2014


Equations of Motion for the Out-of-Equilibrium Dynamics of Isolated Quantum Systems from the Projection Operator Technique
journal, December 2014


Prethermalization and Thermalization in Models with Weak Integrability Breaking
journal, October 2015


Thermalization and light cones in a model with weak integrability breaking
journal, December 2016


Matrix-valued Boltzmann equation for the Hubbard chain
journal, September 2012


Matrix-valued Boltzmann equation for the nonintegrable Hubbard chain
journal, July 2013


Thermalization rates in the one-dimensional Hubbard model with next-to-nearest neighbor hopping
journal, March 2017


Hamiltonian truncation approach to quenches in the Ising field theory
journal, October 2016


Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states
journal, May 2006


Local integrals of motion in many-body localized systems: Local integrals of motion in many-body localized systems
journal, May 2017

  • Imbrie, John Z.; Ros, Valentina; Scardicchio, Antonello
  • Annalen der Physik, Vol. 529, Issue 7
  • DOI: 10.1002/andp.201600278

Rare-region effects and dynamics near the many-body localization transition: Rare-region effects and dynamics near the many-body localization transition
journal, January 2017

  • Agarwal, Kartiek; Altman, Ehud; Demler, Eugene
  • Annalen der Physik, Vol. 529, Issue 7
  • DOI: 10.1002/andp.201600326

Many-body localization in incommensurate models with a mobility edge: Many-body localization in incommensurate models with a mobility edge
journal, May 2017

  • Deng, Dong-Ling; Ganeshan, Sriram; Li, Xiaopeng
  • Annalen der Physik, Vol. 529, Issue 7
  • DOI: 10.1002/andp.201600399

Recent progress in many-body localization: Recent progress in many-body localization
journal, July 2017


Many-body localization: An introduction and selected topics
journal, September 2018


Obtaining Highly Excited Eigenstates of Many-Body Localized Hamiltonians by the Density Matrix Renormalization Group Approach
journal, June 2016


Finding Matrix Product State Representations of Highly Excited Eigenstates of Many-Body Localized Hamiltonians
journal, January 2017


On Many-Body Localization for Quantum Spin Chains
journal, April 2016


Two-dimensional Ising field theory in a magnetic field: Breakup of the cut in the two-point function
journal, August 1978


Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
journal, February 1944


INTEGRALS OF MOTION AND S-MATRIX OF THE (SCALED) T = T c ISING MODEL WITH MAGNETIC FIELD
journal, October 1989


Non-integrable quantum field theories as perturbations of certain integrable models
journal, August 1996


Non-integrable aspects of the multi-frequency sine-Gordon model
journal, April 1998


Confinement in the Bulk, Deconfinement on the Wall: Infrared Equivalence between Compactified QCD and Quantum Magnets
journal, September 2017


Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E 8 Symmetry
journal, January 2010


Spinon confinement in the one-dimensional Ising-like antiferromagnet SrCo 2 V 2 O 8
journal, April 2015


From confined spinons to emergent fermions: Observation of elementary magnetic excitations in a transverse-field Ising chain
journal, September 2016


Nonthermal States Arising from Confinement in One and Two Dimensions
journal, April 2019


Truncated Comformal Space Approach to Scaling Lee-Yang Model
journal, August 1990

  • Yurov, V. P.; Zamolodchikov, Al. B.
  • International Journal of Modern Physics A, Vol. 05, Issue 16
  • DOI: 10.1142/S0217751X9000218X

Truncated-Fermionic-Space Approach to the Critical 2d Ising Model with Magnetic Field
journal, October 1991

  • Yurov, V. P.; Zamolodchikov, Al. B.
  • International Journal of Modern Physics A, Vol. 06, Issue 25
  • DOI: 10.1142/S0217751X91002161

Numerical Renormalization Group for Continuum One-Dimensional Systems
journal, April 2007


Renormalization Group for Treating 2D Coupled Arrays of Continuum 1D Systems
journal, March 2009


Energy level distribution of perturbed conformal field theories
journal, July 2010

  • Brandino, G. P.; Konik, R. M.; Mussardo, G.
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2010, Issue 07
  • DOI: 10.1088/1742-5468/2010/07/P07013

Quench dynamics of the Ising field theory in a magnetic field
journal, January 2018


Construction of Green's functions from an exact S matrix
journal, April 1979


Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at . Perturbative analysis
journal, August 2011


Characterization of resonances using finite size effects
journal, August 2006


Real-time confinement following a quantum quench to a non-integrable model
journal, November 2016

  • Kormos, Marton; Collura, Mario; Takács, Gabor
  • Nature Physics, Vol. 13, Issue 3
  • DOI: 10.1038/nphys3934

Relaxation of a one-dimensional Mott insulator after an interaction quench
journal, July 2008


Correlation spreading and properties of the quantum state in quench dynamics
journal, June 2018


Bound states and E 8 symmetry effects in perturbed quantum Ising chains
journal, January 2011


Quasiparticle breakdown in the quasi-one-dimensional Ising ferromagnet CoNb 2 O 6
journal, November 2014


Strong and Weak Thermalization of Infinite Nonintegrable Quantum Systems
journal, February 2011


Ballistic Spreading of Entanglement in a Diffusive Nonintegrable System
journal, September 2013


Slowest local operators in quantum spin chains
journal, July 2015


Thermalization of entanglement
journal, June 2015


Quasiparticle explanation of the weak-thermalization regime under quench in a nonintegrable quantum spin chain
journal, February 2017


The density-matrix renormalization group in the age of matrix product states
journal, January 2011


Studying Two-Dimensional Systems with the Density Matrix Renormalization Group
journal, March 2012


Holographic quenches in a confined phase
journal, November 2017

  • Myers, Robert C.; Rozali, Moshe; Way, Benson
  • Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 49
  • DOI: 10.1088/1751-8121/aa927c

Matrix Product States for Gauge Field Theories
journal, August 2014


Confinement and String Breaking for QED 2 in the Hamiltonian Picture
journal, November 2016


Chiral condensate in the Schwinger model with matrix product operators
journal, May 2016


Real-time simulation of the Schwinger effect with matrix product states
journal, December 2017


Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks
journal, May 2017


Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
journal, February 2017


Many-Body Localization with Long-Range Interactions
journal, October 2017


Symmetry breaking and localization in a random Schwinger model with commensuration
journal, September 2018


Confinement in the q-state Potts model: an RG-TCSA study
journal, September 2015


Understanding the entanglement entropy and spectra of 2D quantum systems through arrays of coupled 1D chains
journal, June 2013


The ALPS project release 1.3: Open-source software for strongly correlated systems
journal, March 2007

  • Albuquerque, A. F.; Alet, F.; Corboz, P.
  • Journal of Magnetism and Magnetic Materials, Vol. 310, Issue 2
  • DOI: 10.1016/j.jmmm.2006.10.304