Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1406.4902 · Physical Review A

Quench between a Mott insulator and a Lieb-Liniger liquid

Garry Goldstein, Natan Andrei

Published Oct 23, 2014• 10 citations
arXivHTMLPDF

Abstract

In this work we study a quench between a Mott insulator and a repulsive Lieb-Liniger liquid. We explicitly find the stationary state when a long time has passed after the quench. It is given by a generalized Gibbs ensemble (GGE) density matrix, which we completely characterize, calculating the quasiparticle density that describes the system after the quench. In the long-time limit we find an explicit form for the local three-body density-density-density correlation function and the asymptotic long-distance limit of the two-point density-density correlation function. The latter is shown to have Gaussian decay at large distances.

DOI
10.1103/physreva.90.043626

Related papers

Equilibration and generalized Gibbs ensemble for hard wall boundary conditions

Garry Goldstein, Natan Andrei

In this work we present an analysis of a quench for the repulsive Lieb-Liniger gas confined to a large box with hard wall boundary conditions. We study the time average of local correlation functions and show that both the quench action approach and the generalized Gibbs ensemble formalism are applicable for the long-time average of local correlation functions. We find that the time average of the system corresponds to an eigenstate of the Lieb-Liniger Hamiltonian and that this eigenstate is related to an eigenstate of a Lieb-Liniger Hamiltonian with periodic boundary conditions on an interval of twice the length and with twice as many particles (a doubled system). We further show that local operators with support far away from the boundaries of the hard wall have the same expectation values with respect to this eigenstate as corresponding operators for the doubled system. We present an example of a quench where the gas is initially confined in several moving traps and then released into a bigger container, an approximate description of the Newton's cradle experiment. We calculate the time average of various correlation functions for long times after the quench.

arXiv:1505.02585•Physical Review B•Oct 1, 2015•23 citations

Interaction quenches in the Lieb-Liniger model

Márton Kormos, Aditya Shashi, Yang-Zhi Chou +1 more

We obtain exact results on interaction quenches in the 1D Bose gas described by the integrable Lieb-Liniger model. We show that in the long time limit integrability leads to significant deviations from the predictions of the grand canonical ensemble and a description within the generalized Gibbs ensemble (GGE) is needed. For a non-interacting initial state and arbitrary final interactions, we find that the presence of infinitely many conserved charges generates a non-analytic behavior in the equilibrated density of quasimomenta. This manifests itself in a dynamically generated Friedel-like oscillation of the non-local correlation functions with interaction dependent oscillation momenta. We also exactly evaluate local correlations and the generalized chemical potentials within GGE.

arXiv:1204.3889•Apr 17, 2012•4 citations

Failure of the Quench Action Formalism for Mott Insulator Initial States

Garry Goldstein

The quench action formalism relies on the assumption that the overlap between a generic initial state $\left|Ψ_{0}\right\rangle $ and an eigenstate of an integrable model - defined through the rapidities $\left|k_{1},...k_{N}\right\rangle $ - can be written as: \begin{equation} \left\langle k_{1},...k_{N}\midΨ_{0}\right\rangle =\exp\left(-S_{Ψ_{0}}\left(ρ\left(k\right)\right)\right),\label{eq:Exponential} \end{equation} where $ρ\left(k\right)$ is the quasiparticle density of the state $\left|k_{1},...k_{N}\right\rangle $ and $S_{Ψ_{0}}$ is some smooth function of $ρ\left(k\right)$ that depends on $Ψ_{0}$. In particular the quench action formalism assumes the overlap depends smoothly on the quasiparticle density $ρ\left(k\right)$. In this work, by explicit counter example, we show that this is not the case. We consider the quench between a Mott insulator and a Lieb Liniger gas. We show that the overlap between the ground state of the Mott insulator and arbitrary eigenstates of the Lieb Liniger gas has a highly singular behavior and no expression like Eq. (1) applies. We do so within the Tonks Girardeau limit of the Lieb Liniger gas and to leading order in the $1/c$ expansion for the overlap (with $c$ being the coupling constant of the Lieb Liniger gas). In the Appendix we show similar results for overlaps in the XXZ model with crystal states.

arXiv:2606.07111•Jun 5, 2026•0 citations

Quantum Quench in the Transverse-Field Ising Chain

Pasquale Calabrese, Fabian H. L. Eßler, Maurizio Fagotti

We consider the time evolution of observables in the transverse-field Ising chain after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.

arXiv:1104.0154•Physical Review Letters•Jun 2, 2011•685 citations

Dynamical Correlation of the Post-quench Non-thermal Equilibrium State

Yang-Yang Chen, Song Cheng

After a quantum quench, the integrable system is expected to relax to a non-thermal equilibrium state (NTES) whose local properties are believed to be governed by a generalized Gibbs ensemble (GGE). Combining quench action and the form factor approach, we compute the field-field correlation in the NTES produced by an interaction quench of the Lieb-Liniger model. The spectral distribution is shown to be qualitatively different from that of a thermal equilibrium state (TES): a new dispersion branch appears whose microscopic mechanism can be traced to the algebraic decaying tail for the root density distribution function, and indicates the existence of a broader family of NTES featuring similar spectral property.

quant-pharXiv:2601.06987•Jan 13, 2026•0 citations

Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

Jan C. Zill, Tod M. Wright, Karen V. Kheruntsyan +2 more

We investigate the relaxation dynamics of the integrable Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The system is initially prepared in its noninteracting ground state and the interaction strength is then abruptly switched to a positive value, corresponding to repulsive interactions between the bosons. We calculate equal-time correlation functions of the nonequilibrium Bose field for small systems of up to five particles via symbolic evaluation of coordinate Bethe-ansatz expressions for operator matrix elements between Lieb-Liniger eigenstates. We characterize the relaxation of the system by comparing the time-evolving correlation functions following the quench to the equilibrium correlations predicted by the diagonal ensemble and relate the behavior of these correlations to that of the quantum fidelity between the many-body wave function and the initial state of the system. Our results for the asymptotic scaling of local second-order correlations with increasing interaction strength agree with the predictions of recent generalized thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations obtained within our approach exhibit a markedly different power-law dependence on the interaction strength as the Tonks-Girardeau limit of infinitely strong interactions is approached.

arXiv:1407.4998•Physical Review A•Feb 12, 2015•43 citations
In this work we study a quench between a Mott insulator and a repulsive Lieb-Liniger liquid. We explicitly find the stationary state when a long time has passed after the quench. It is given by a generalized Gibbs ensemble (GGE) density matrix, which we completely characterize, calculating the quasiparticle density that describes the system after the quench. In the long-time limit we find an explicit form for the local three-body density-density-density correlation function and the asymptotic long-distance limit of the two-point density-density correlation function. The latter is shown to have Gaussian decay at large distances.
In this work we present an analysis of a quench for the repulsive Lieb-Liniger gas confined to a large box with hard wall boundary conditions. We study the time average of local correlation functions and show that both the quench action approach and the generalized Gibbs ensemble formalism are applicable for the long-time average of local correlation functions. We find that the time average of the system corresponds to an eigenstate of the Lieb-Liniger Hamiltonian and that this eigenstate is related to an eigenstate of a Lieb-Liniger Hamiltonian with periodic boundary conditions on an interval of twice the length and with twice as many particles (a doubled system). We further show that local operators with support far away from the boundaries of the hard wall have the same expectation values with respect to this eigenstate as corresponding operators for the doubled system. We present an example of a quench where the gas is initially confined in several moving traps and then released into a bigger container, an approximate description of the Newton's cradle experiment. We calculate the time average of various correlation functions for long times after the quench.
We obtain exact results on interaction quenches in the 1D Bose gas described by the integrable Lieb-Liniger model. We show that in the long time limit integrability leads to significant deviations from the predictions of the grand canonical ensemble and a description within the generalized Gibbs ensemble (GGE) is needed. For a non-interacting initial state and arbitrary final interactions, we find that the presence of infinitely many conserved charges generates a non-analytic behavior in the equilibrated density of quasimomenta. This manifests itself in a dynamically generated Friedel-like oscillation of the non-local correlation functions with interaction dependent oscillation momenta. We also exactly evaluate local correlations and the generalized chemical potentials within GGE.
The quench action formalism relies on the assumption that the overlap between a generic initial state $\left|Ψ_{0}\right\rangle $ and an eigenstate of an integrable model - defined through the rapidities $\left|k_{1},...k_{N}\right\rangle $ - can be written as: \begin{equation} \left\langle k_{1},...k_{N}\midΨ_{0}\right\rangle =\exp\left(-S_{Ψ_{0}}\left(ρ\left(k\right)\right)\right),\label{eq:Exponential} \end{equation} where ρ(k)ρ\left(k\right)ρ(k) is the quasiparticle density of the state $\left|k_{1},...k_{N}\right\rangle $ and SΨ0S_{Ψ_{0}}SΨ0​​ is some smooth function of ρ(k)ρ\left(k\right)ρ(k) that depends on Ψ0Ψ_{0}Ψ0​. In particular the quench action formalism assumes the overlap depends smoothly on the quasiparticle density ρ(k)ρ\left(k\right)ρ(k). In this work, by explicit counter example, we show that this is not the case. We consider the quench between a Mott insulator and a Lieb Liniger gas. We show that the overlap between the ground state of the Mott insulator and arbitrary eigenstates of the Lieb Liniger gas has a highly singular behavior and no expression like Eq. (1) applies. We do so within the Tonks Girardeau limit of the Lieb Liniger gas and to leading order in the 1/c1/c1/c expansion for the overlap (with ccc being the coupling constant of the Lieb Liniger gas). In the Appendix we show similar results for overlaps in the XXZ model with crystal states.
We consider the time evolution of observables in the transverse-field Ising chain after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.
After a quantum quench, the integrable system is expected to relax to a non-thermal equilibrium state (NTES) whose local properties are believed to be governed by a generalized Gibbs ensemble (GGE). Combining quench action and the form factor approach, we compute the field-field correlation in the NTES produced by an interaction quench of the Lieb-Liniger model. The spectral distribution is shown to be qualitatively different from that of a thermal equilibrium state (TES): a new dispersion branch appears whose microscopic mechanism can be traced to the algebraic decaying tail for the root density distribution function, and indicates the existence of a broader family of NTES featuring similar spectral property.
We investigate the relaxation dynamics of the integrable Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The system is initially prepared in its noninteracting ground state and the interaction strength is then abruptly switched to a positive value, corresponding to repulsive interactions between the bosons. We calculate equal-time correlation functions of the nonequilibrium Bose field for small systems of up to five particles via symbolic evaluation of coordinate Bethe-ansatz expressions for operator matrix elements between Lieb-Liniger eigenstates. We characterize the relaxation of the system by comparing the time-evolving correlation functions following the quench to the equilibrium correlations predicted by the diagonal ensemble and relate the behavior of these correlations to that of the quantum fidelity between the many-body wave function and the initial state of the system. Our results for the asymptotic scaling of local second-order correlations with increasing interaction strength agree with the predictions of recent generalized thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations obtained within our approach exhibit a markedly different power-law dependence on the interaction strength as the Tonks-Girardeau limit of infinitely strong interactions is approached.