Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model
Abstract
Here, we consider the construction of a generalized Gibbs ensemble composed of complete bases of conserved charges in the repulsive Lieb-Liniger model. We will show that it is possible to construct these bases with varying locality as well as demonstrating that such constructions are always possible provided one has in hand at least one complete basis set of charges. This procedure enables the construction of bases of charges that possess well-defined, finite expectation values given an arbitrary initial state. We demonstrate the use of these charges in the context of two different quantum quenches: a quench where the strength of the interactions in a one-dimensional gas is switched suddenly from zero to some finite value and the release of a one-dimensional cold atomic gas from a confining parabolic trap. While we focus on the Lieb-Liniger model in this paper, the principle of the construction of these charges applies to all integrable models, both in continuum and lattice form.
- Authors:
-
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Publication Date:
- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1489349
- Alternate Identifier(s):
- OSTI ID: 1483031
- Report Number(s):
- BNL-210827-2018-JAAM
Journal ID: ISSN 2470-0045; PLEEE8
- Grant/Contract Number:
- SC0012704
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review E
- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 5; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Palmai, Tamas, and Konik, R. M. Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model. United States: N. p., 2018.
Web. doi:10.1103/PhysRevE.98.052126.
Palmai, Tamas, & Konik, R. M. Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model. United States. https://doi.org/10.1103/PhysRevE.98.052126
Palmai, Tamas, and Konik, R. M. Wed .
"Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model". United States. https://doi.org/10.1103/PhysRevE.98.052126. https://www.osti.gov/servlets/purl/1489349.
@article{osti_1489349,
title = {Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model},
author = {Palmai, Tamas and Konik, R. M.},
abstractNote = {Here, we consider the construction of a generalized Gibbs ensemble composed of complete bases of conserved charges in the repulsive Lieb-Liniger model. We will show that it is possible to construct these bases with varying locality as well as demonstrating that such constructions are always possible provided one has in hand at least one complete basis set of charges. This procedure enables the construction of bases of charges that possess well-defined, finite expectation values given an arbitrary initial state. We demonstrate the use of these charges in the context of two different quantum quenches: a quench where the strength of the interactions in a one-dimensional gas is switched suddenly from zero to some finite value and the release of a one-dimensional cold atomic gas from a confining parabolic trap. While we focus on the Lieb-Liniger model in this paper, the principle of the construction of these charges applies to all integrable models, both in continuum and lattice form.},
doi = {10.1103/PhysRevE.98.052126},
journal = {Physical Review E},
number = 5,
volume = 98,
place = {United States},
year = {Wed Nov 21 00:00:00 EST 2018},
month = {Wed Nov 21 00:00:00 EST 2018}
}
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Works referenced in this record:
Quantum quenches in the transverse field Ising chain: II. Stationary state properties
journal, July 2012
- Calabrese, Pasquale; Essler, Fabian H. L.; Fagotti, Maurizio
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 07
Fermi-Bose mapping for one-dimensional Bose gases
journal, August 2005
- Yukalov, V. I.; Girardeau, M. D.
- Laser Physics Letters, Vol. 2, Issue 8
Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008
- Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim
- Nature, Vol. 452, Issue 7189
Generalized Gibbs ensemble in integrable lattice models
journal, June 2016
- Vidmar, Lev; Rigol, Marcos
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6
The Quench Action
journal, June 2016
- Caux, Jean-Sébastien
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6
Quantum quenches to the attractive one-dimensional Bose gas: exact results
journal, January 2016
- Piroli, Lorenzo; Calabrese, Pasquale; Essler, Fabian
- SciPost Physics, Vol. 1, Issue 1
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
Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
journal, September 2014
- Wouters, B.; De Nardis, J.; Brockmann, M.
- Physical Review Letters, Vol. 113, Issue 11
Dynamical Correlations After a Quantum Quench
journal, December 2012
- Essler, Fabian H. L.; Evangelisti, Stefano; Fagotti, Maurizio
- Physical Review Letters, Vol. 109, Issue 24
Quench dynamics and relaxation in isolated integrable quantum spin chains
journal, June 2016
- Essler, Fabian H. L.; Fagotti, Maurizio
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6
Correlations after Quantum Quenches in the Spin Chain: Failure of the Generalized Gibbs Ensemble
journal, September 2014
- Pozsgay, B.; Mestyán, M.; Werner, M. A.
- Physical Review Letters, Vol. 113, Issue 11
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
Exact steady states for quantum quenches in integrable Heisenberg spin chains
journal, August 2016
- Piroli, Lorenzo; Vernier, Eric; Calabrese, Pasquale
- Physical Review B, Vol. 94, Issue 5
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
journal, April 2016
- Gogolin, Christian; Eisert, Jens
- Reports on Progress in Physics, Vol. 79, Issue 5
Constructing the Generalized Gibbs Ensemble after a Quantum Quench
journal, October 2012
- Caux, Jean-Sébastien; Konik, Robert M.
- Physical Review Letters, Vol. 109, Issue 17
Realization of an Excited, Strongly Correlated Quantum Gas Phase
journal, September 2009
- Haller, E.; Gustavsson, M.; Mark, M. J.
- Science, Vol. 325, Issue 5945
Failure of the generalized eigenstate thermalization hypothesis in integrable models with multiple particle species
journal, September 2014
- Pozsgay, B.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 9
Interaction Quench in the Hubbard Model
journal, May 2008
- Moeckel, Michael; Kehrein, Stefan
- Physical Review Letters, Vol. 100, Issue 17
Zamolodchikov–Faddeev algebra and quantum quenches in integrable field theories
journal, February 2012
- Sotiriadis, S.; Fioretto, D.; Mussardo, G.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 02
Infinite-Time Average of Local Fields in an Integrable Quantum Field Theory After a Quantum Quench
journal, September 2013
- Mussardo, G.
- Physical Review Letters, Vol. 111, Issue 10
Strong and Weak Thermalization of Infinite Nonintegrable Quantum Systems
journal, February 2011
- Bañuls, M. C.; Cirac, J. I.; Hastings, M. B.
- Physical Review Letters, Vol. 106, Issue 5
Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons
journal, February 2007
- Rigol, Marcos; Dunjko, Vanja; Yurovsky, Vladimir
- Physical Review Letters, Vol. 98, Issue 5
Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
journal, December 2014
- Brockmann, M.; Wouters, B.; Fioretto, D.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 12
Generalized Thermalization in an Integrable Lattice System
journal, April 2011
- Cassidy, Amy C.; Clark, Charles W.; Rigol, Marcos
- Physical Review Letters, Vol. 106, Issue 14
Motion of a Distinguishable Impurity in the Bose Gas: Arrested Expansion Without a Lattice and Impurity Snaking
journal, April 2016
- Robinson, Neil J.; Caux, Jean-Sébastien; Konik, Robert M.
- Physical Review Letters, Vol. 116, Issue 14
Momentum relaxation of a mobile impurity in a one-dimensional quantum gas
journal, April 2014
- Burovski, E.; Cheianov, V.; Gamayun, O.
- Physical Review A, Vol. 89, Issue 4
Thermalization near Integrability in a Dipolar Quantum Newton’s Cradle
journal, May 2018
- Tang, Yijun; Kao, Wil; Li, Kuan-Yu
- Physical Review X, Vol. 8, Issue 2
Quasilocal Conserved Operators in the Isotropic Heisenberg Spin- Chain
journal, September 2015
- Ilievski, Enej; Medenjak, Marko; Prosen, Tomaž
- Physical Review Letters, Vol. 115, Issue 12
Thermalization and quantum correlations in exactly solvable models
journal, January 2012
- Cazalilla, Miguel A.; Iucci, Anibal; Chung, Ming-Chiang
- Physical Review E, Vol. 85, Issue 1
Quantum chaos and thermalization in gapped systems
journal, July 2010
- Rigol, Marcos; Santos, Lea F.
- Physical Review A, Vol. 82, Issue 1
Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain
journal, September 2012
- Foini, Laura; Cugliandolo, Leticia F.; Gambassi, Andrea
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 09
Quantum quenches in the sinh-Gordon model: steady state and one-point correlation functions
journal, June 2016
- Bertini, Bruno; Piroli, Lorenzo; Calabrese, Pasquale
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6
Local conservation laws in spin-$\frac{1}{2}$ XY chains with open boundary conditions
journal, June 2016
- Fagotti, Maurizio
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6
Generalized Gibbs ensemble and work statistics of a quenched Luttinger liquid
journal, October 2012
- Dóra, Balázs; Bácsi, Ádám; Zaránd, Gergely
- Physical Review B, Vol. 86, Issue 16
Quantum Quench in the Transverse-Field Ising Chain
journal, June 2011
- Calabrese, Pasquale; Essler, Fabian H. L.; Fagotti, Maurizio
- Physical Review Letters, Vol. 106, Issue 22
Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
journal, February 2006
- Cherny, Alexander Yu.; Brand, Joachim
- Physical Review A, Vol. 73, Issue 2
Density form factors of the 1D Bose gas for finite entropy states
journal, February 2015
- De Nardis, J.; Panfil, M.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2015, Issue 2
Quantum Quenches in the Thermodynamic Limit
journal, April 2014
- Rigol, M.
- Physical Review Letters, Vol. 112, Issue 17
String-charge duality in integrable lattice models
journal, June 2016
- Ilievski, Enej; Quinn, Eoin; De Nardis, Jacopo
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6
Probing non-thermal density fluctuations in the one-dimensional Bose gas
journal, January 2017
- De Nardis, Jacopo; Panfil, Milosz; Gambassi, Andrea
- SciPost Physics, Vol. 3, Issue 3
Finite-size effects from higher conservation laws for the one-dimensional Bose gas
journal, May 2013
- Eriksson, Erik; Korepin, Vladimir
- Journal of Physics A: Mathematical and Theoretical, Vol. 46, Issue 23
Quantum Inverse Scattering Method and Correlation Functions
book, January 2010
- Korepin, V. E.; Bogoliubov, N. M.; Izergin, A. G.
- Cambridge University Press
Relaxation after quantum quenches in the spin- Heisenberg XXZ chain
journal, March 2014
- Fagotti, Maurizio; Collura, Mario; Essler, Fabian H. L.
- Physical Review B, Vol. 89, Issue 12
Quantum flutter of supersonic particles in one-dimensional quantum liquids
journal, October 2012
- Mathy, Charles J. M.; Zvonarev, Mikhail B.; Demler, Eugene
- Nature Physics, Vol. 8, Issue 12
Long time dynamics following a quench in an integrable quantum spin chain: Local versus nonlocal operators and effective thermal behavior
journal, October 2010
- Rossini, Davide; Suzuki, Sei; Mussardo, Giuseppe
- Physical Review B, Vol. 82, Issue 14
Failure of the local generalized Gibbs ensemble for integrable models with bound states
journal, October 2014
- Goldstein, Garry; Andrei, Natan
- Physical Review A, Vol. 90, Issue 4
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases
journal, December 2015
- Brandino, G. P.; Caux, J. -S.; Konik, R. M.
- Physical Review X, Vol. 5, Issue 4
Exact time evolution of space- and time-dependent correlation functions after an interaction quench in the one-dimensional Bose gas
journal, July 2012
- Mossel, Jorn; Caux, Jean-Sébastien
- New Journal of Physics, Vol. 14, Issue 7
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum
journal, May 1963
- Lieb, Elliott H.
- Physical Review, Vol. 130, Issue 4
Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
journal, February 2017
- Bastianello, Alvise; Sotiriadis, Spyros
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 2
From interacting particles to equilibrium statistical ensembles
journal, March 2017
- Ilievski, Enej; Quinn, Eoin; Caux, Jean-Sébastien
- Physical Review B, Vol. 95, Issue 11
Quench action and Rényi entropies in integrable systems
journal, September 2017
- Alba, Vincenzo; Calabrese, Pasquale
- Physical Review B, Vol. 96, Issue 11
Quantum quenches in integrable field theories
journal, May 2010
- Fioretto, Davide; Mussardo, Giuseppe
- New Journal of Physics, Vol. 12, Issue 5
Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
journal, April 2015
- Mestyán, M.; Pozsgay, B.; Takács, G.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2015, Issue 4
Higher conservation laws for the quantum non-linear Schrödinger equation
journal, August 1990
- Davies, B.
- Physica A: Statistical Mechanics and its Applications, Vol. 167, Issue 2
Density ripples in expanding low-dimensional gases as a probe of correlations
journal, September 2009
- Imambekov, A.; Mazets, I. E.; Petrov, D. S.
- Physical Review A, Vol. 80, Issue 3
Effective Thermal Dynamics Following a Quantum Quench in a Spin Chain
journal, March 2009
- Rossini, Davide; Silva, Alessandro; Mussardo, Giuseppe
- Physical Review Letters, Vol. 102, Issue 12
Quantum quench dynamics of the Luttinger model
journal, December 2009
- Iucci, A.; Cazalilla, M. A.
- Physical Review A, Vol. 80, Issue 6
Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling
journal, August 2015
- Meinert, F.; Panfil, M.; Mark, M. J.
- Physical Review Letters, Vol. 115, Issue 8
Analytic results for a quantum quench from free to hard-core one-dimensional bosons
journal, January 2014
- Kormos, Márton; Collura, Mario; Calabrese, Pasquale
- Physical Review A, Vol. 89, Issue 1
From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
journal, May 2016
- D'Alessio, Luca; Kafri, Yariv; Polkovnikov, Anatoli
- Advances in Physics, Vol. 65, Issue 3
Fermion-Boson Duality of One-Dimensional Quantum Particles with Generalized Contact Interactions
journal, March 1999
- Cheon, Taksu; Shigehara, T.
- Physical Review Letters, Vol. 82, Issue 12
Experimental observation of a generalized Gibbs ensemble
journal, April 2015
- Langen, T.; Erne, S.; Geiger, R.
- Science, Vol. 348, Issue 6231
The approach to thermal equilibrium in quantized chaotic systems
journal, January 1999
- Srednicki, Mark
- Journal of Physics A: Mathematical and General, Vol. 32, Issue 7
Asymptotic Representations of Fourier Integrals and the Method of Stationary Phase
journal, March 1955
- Erdelyi, A.
- Journal of the Society for Industrial and Applied Mathematics, Vol. 3, Issue 1
Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
journal, May 1963
- Lieb, Elliott H.; Liniger, Werner
- Physical Review, Vol. 130, Issue 4
Interaction quenches in the one-dimensional Bose gas
journal, November 2013
- Kormos, Márton; Shashi, Aditya; Chou, Yang-Zhi
- Physical Review B, Vol. 88, Issue 20
Solution for an interaction quench in the Lieb-Liniger Bose gas
journal, March 2014
- De Nardis, Jacopo; Wouters, Bram; Brockmann, Michael
- Physical Review A, Vol. 89, Issue 3
Validity of the GGE for quantum quenches from interacting to noninteracting models
journal, July 2014
- Sotiriadis, Spyros; Calabrese, Pasquale
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 7
On generalized Gibbs ensembles with an infinite set of conserved charges
journal, September 2017
- Pozsgay, B.; Vernier, E.; Werner, M. A.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 9
On truncated generalized Gibbs ensembles in the Ising field theory
journal, January 2017
- Essler, F. H. L.; Mussardo, G.; Panfil, M.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 1
Measuring effective temperatures in a generalized Gibbs ensemble
journal, May 2017
- Foini, Laura; Gambassi, Andrea; Konik, Robert
- Physical Review E, Vol. 95, Issue 5
Time Evolution of Local Observables After Quenching to an Integrable Model
journal, June 2013
- Caux, Jean-Sébastien; Essler, Fabian H. L.
- Physical Review Letters, Vol. 110, Issue 25
Absence of Thermalization in Nonintegrable Systems
journal, January 2011
- Gogolin, Christian; Müller, Markus P.; Eisert, Jens
- Physical Review Letters, Vol. 106, Issue 4
Generalized Gibbs ensembles for quantum field theories
journal, May 2015
- Essler, F. H. L.; Mussardo, G.; Panfil, M.
- Physical Review A, Vol. 91, Issue 5
Dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit
journal, September 2005
- Brand, Joachim; Cherny, Alexander Yu.
- Physical Review A, Vol. 72, Issue 3
Quantum quench in the transverse field Ising chain: I. Time evolution of order parameter correlators
journal, July 2012
- Calabrese, Pasquale; Essler, Fabian H. L.; Fagotti, Maurizio
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 07
Relaxation dynamics in the gapped XXZ spin-1/2 chain
journal, May 2010
- Mossel, Jorn; Caux, Jean-Sébastien
- New Journal of Physics, Vol. 12, Issue 5
Mean values of local operators in highly excited Bethe states
journal, January 2011
- Pozsgay, Balázs
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2011, Issue 01
Exact solution for the quench dynamics of a nested integrable system
journal, August 2017
- Mestyán, Márton; Bertini, Bruno; Piroli, Lorenzo
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 8
Quantum quench in the infinitely repulsive Hubbard model: the stationary state
journal, October 2017
- Bertini, Bruno; Tartaglia, Elena; Calabrese, Pasquale
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 10
Equilibration of a Tonks-Girardeau Gas Following a Trap Release
journal, June 2013
- Collura, Mario; Sotiriadis, Spyros; Calabrese, Pasquale
- Physical Review Letters, Vol. 110, Issue 24
Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering
journal, January 2017
- Vernier, Eric; Cortés Cubero, Axel
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 2
Complete Generalized Gibbs Ensembles in an Interacting Theory
journal, October 2015
- Ilievski, E.; De Nardis, J.; Wouters, B.
- Physical Review Letters, Vol. 115, Issue 15
Thermal fluctuations in quantized chaotic systems
journal, February 1996
- Srednicki, Mark
- Journal of Physics A: Mathematical and General, Vol. 29, Issue 4
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
Quantum statistical mechanics in a closed system
journal, February 1991
- Deutsch, J. M.
- Physical Review A, Vol. 43, Issue 4
Chaos and quantum thermalization
journal, August 1994
- Srednicki, Mark
- Physical Review E, Vol. 50, Issue 2
Dynamics of Excitations in a One-Dimensional Bose Liquid
journal, September 2007
- Khodas, M.; Pustilnik, M.; Kamenev, A.
- Physical Review Letters, Vol. 99, Issue 11
Quench dynamics of a Tonks–Girardeau gas released from a harmonic trap
journal, September 2013
- Collura, Mario; Sotiriadis, Spyros; Calabrese, Pasquale
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2013, Issue 09
Multiparticle Bound-State Formation following a Quantum Quench to the One-Dimensional Bose Gas with Attractive Interactions
journal, February 2016
- Piroli, Lorenzo; Calabrese, Pasquale; Essler, Fabian H. L.
- Physical Review Letters, Vol. 116, Issue 7
A quantum Newton's cradle
journal, April 2006
- Kinoshita, Toshiya; Wenger, Trevor; Weiss, David S.
- Nature, Vol. 440, Issue 7086
The generalized Gibbs ensemble for Heisenberg spin chains
journal, July 2013
- Pozsgay, Balázs
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2013, Issue 07
Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
journal, December 2010
- Biroli, Giulio; Kollath, Corinna; Läuchli, Andreas M.
- Physical Review Letters, Vol. 105, Issue 25
Works referencing / citing this record:
Towards a generalized hydrodynamics description of Rényi entropies in integrable systems
journal, January 2019
- Alba, Vincenzo
- Physical Review B, Vol. 99, Issue 4