skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on April 5, 2020

Title: Nonthermal States Arising from Confinement in One and Two Dimensions

Abstract

We show that confinement in the quantum Ising model leads to nonthermal eigenstates, in both continuum and lattice theories, in both one (1D) and two dimensions (2D). In the ordered phase, the presence of a confining longitudinal field leads to a profound restructuring of the excitation spectrum, with the low-energy two-particle continuum being replaced by discrete “meson” modes (linearly confined pairs of domain walls). These modes exist far into the spectrum and are atypical, in the sense that expectation values in the state with energy $E$ do not agree with the microcanonical (thermal) ensemble prediction. Single meson states persist above the two-meson threshold due to a surprising lack of hybridization with the (n ≥ 4)-domain wall continuum, a result that survives into the thermodynamic limit and that can be understood from analytical calculations. The presence of such states is revealed in anomalous postquench dynamics, such as the lack of a light cone, the suppression of the growth of entanglement entropy, and the absence of thermalization for some initial states. In conclusion, the nonthermal states are confined to the ordered phase—the disordered (paramagnetic) phase exhibits typical thermalization patterns in both 1D and 2D in the absence of integrability.

Authors:
 [1]; ORCiD logo [2];  [3]
  1. Univ. College London, London (United Kingdom); The Open Univ., Milton Keynes (United Kingdom)
  2. Brookhaven National Lab. (BNL), Upton, NY (United States)
  3. Univ. of Amsterdam, Amsterdam (Netherlands)
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:
1529073
Alternate Identifier(s):
OSTI ID: 1505249
Report Number(s):
BNL-211780-2019-JAAM
Journal ID: ISSN 0031-9007; PRLTAO
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 122; Journal Issue: 13; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

James, Andrew J. A., Konik, Robert M., and Robinson, Neil J. Nonthermal States Arising from Confinement in One and Two Dimensions. United States: N. p., 2019. Web. doi:10.1103/PhysRevLett.122.130603.
James, Andrew J. A., Konik, Robert M., & Robinson, Neil J. Nonthermal States Arising from Confinement in One and Two Dimensions. United States. doi:10.1103/PhysRevLett.122.130603.
James, Andrew J. A., Konik, Robert M., and Robinson, Neil J. Fri . "Nonthermal States Arising from Confinement in One and Two Dimensions". United States. doi:10.1103/PhysRevLett.122.130603.
@article{osti_1529073,
title = {Nonthermal States Arising from Confinement in One and Two Dimensions},
author = {James, Andrew J. A. and Konik, Robert M. and Robinson, Neil J.},
abstractNote = {We show that confinement in the quantum Ising model leads to nonthermal eigenstates, in both continuum and lattice theories, in both one (1D) and two dimensions (2D). In the ordered phase, the presence of a confining longitudinal field leads to a profound restructuring of the excitation spectrum, with the low-energy two-particle continuum being replaced by discrete “meson” modes (linearly confined pairs of domain walls). These modes exist far into the spectrum and are atypical, in the sense that expectation values in the state with energy $E$ do not agree with the microcanonical (thermal) ensemble prediction. Single meson states persist above the two-meson threshold due to a surprising lack of hybridization with the (n ≥ 4)-domain wall continuum, a result that survives into the thermodynamic limit and that can be understood from analytical calculations. The presence of such states is revealed in anomalous postquench dynamics, such as the lack of a light cone, the suppression of the growth of entanglement entropy, and the absence of thermalization for some initial states. In conclusion, the nonthermal states are confined to the ordered phase—the disordered (paramagnetic) phase exhibits typical thermalization patterns in both 1D and 2D in the absence of integrability.},
doi = {10.1103/PhysRevLett.122.130603},
journal = {Physical Review Letters},
number = 13,
volume = 122,
place = {United States},
year = {2019},
month = {4}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on April 5, 2020
Publisher's Version of Record

Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

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


Generalized Gibbs ensemble in integrable lattice models
journal, June 2016


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

Many-Body Localization and Thermalization in Quantum Statistical Mechanics
journal, March 2015


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


Many-body localization, symmetry and topology
journal, July 2018


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

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


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


Exact excited states of nonintegrable models
journal, December 2018


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


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


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


Quantum statistical mechanics in a closed system
journal, February 1991


Chaos and quantum thermalization
journal, August 1994


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


The approach to thermal equilibrium in quantized chaotic systems
journal, January 1999


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


Equilibration and thermalization in finite quantum systems
journal, May 2011


Alternatives to Eigenstate Thermalization
journal, March 2012


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


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


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


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


Quench dynamics in randomly generated extended quantum models
journal, June 2012


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


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


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


Dynamical Typicality Approach to Eigenstate Thermalization
journal, June 2018


A quantum Newton's cradle
journal, April 2006

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

Non-equilibrium coherence dynamics in one-dimensional Bose gases
journal, September 2007

  • Hofferberth, S.; Lesanovsky, I.; Fischer, B.
  • Nature, Vol. 449, Issue 7160
  • DOI: 10.1038/nature06149

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

Relaxation and Prethermalization in an Isolated Quantum System
journal, September 2012


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

Local emergence of thermal correlations in an isolated quantum many-body system
journal, September 2013

  • Langen, T.; Geiger, R.; Kuhnert, M.
  • Nature Physics, Vol. 9, Issue 10
  • DOI: 10.1038/nphys2739

Quantum many-body systems out of equilibrium
journal, February 2015

  • Eisert, J.; Friesdorf, M.; Gogolin, C.
  • Nature Physics, Vol. 11, Issue 2
  • DOI: 10.1038/nphys3215

Experimental observation of a generalized Gibbs ensemble
journal, April 2015


Observation of many-body localization of interacting fermions in a quasirandom optical lattice
journal, July 2015


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

Exploring the many-body localization transition in two dimensions
journal, June 2016


Quantum thermalization through entanglement in an isolated many-body system
journal, August 2016


Experimental characterization of a quantum many-body system via higher-order correlations
journal, May 2017

  • Schweigler, Thomas; Kasper, Valentin; Erne, Sebastian
  • Nature, Vol. 545, Issue 7654
  • DOI: 10.1038/nature22310

Attosecond physics
journal, February 2009


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

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


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


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


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


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


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


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

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


Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension
journal, February 2007


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


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


Time Dependence of Correlation Functions Following a Quantum Quench
journal, April 2006


Quantum quenches in extended systems
journal, June 2007


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

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


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


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


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


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


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