Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz
arXiv:1909.04470 · doi:10.21468/SciPostPhys.8.3.034
Abstract
The non-equilibrium steady states of integrable models are believed to be described by the Generalized Gibbs Ensemble (GGE), which involves all local and quasi-local conserved charges of the model. In this work we investigate integrable lattice models solvable by the nested Bethe Ansatz, with group symmetry , . In these models the Bethe Ansatz involves various types of Bethe rapidities corresponding to the "nesting" procedure, describing the internal degrees of freedom for the excitations. We show that a complete set of charges for the GGE can be obtained from the known fusion hierarchy of transfer matrices. The resulting charges are quasi-local in a certain regime in rapidity space, and they completely fix the rapidity distributions of each string type from each nesting level.
47 pages, v2: arguments regarding the inversion of R-matrices modified, conlusions unaltered, v3: minor modifications in the Introduction
References in corpus (55)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Nonequilibrium dynamics of closed interacting quantum systems
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
- Emergent hydrodynamics in integrable quantum systems out of equilibrium
- Time evolution of local observables after quenching to an integrable model
- Complete Generalized Gibbs Ensemble in an interacting Theory
- Dephasing and the steady state in quantum many-particle systems
- Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
- Generalized Thermalization in an Integrable Lattice System
- Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
- Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
- Quasilocal charges in integrable lattice systems
- Reduced Density Matrix after a Quantum Quench
- Quantum quench dynamics of the Luttinger model
- Quantum quench dynamics of some exactly solvable models in one dimension
- Functional Relations in Solvable Lattice Models I: Functional Relations and Representation Theory
- Effective thermal dynamics following a quantum quench in a spin chain
- Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
- What is an integrable quench?
- Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
- Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
- Dynamical Correlations after a Quantum Quench
- Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
- T-systems and Y-systems in integrable systems
- Thermalization and Quantum Correlations in Exactly Solvable Models
- Relaxation of a one-dimensional Mott insulator after an interaction quench
- Introduction to Yangian symmetry in integrable field theory
- Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
- Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
- From Interacting Particles to Equilibrium Statistical Ensembles
- Generalized Gibbs Ensemble for Heisenberg Spin Chains
- Failure of the GGE hypothesis for integrable models with bound states
- String-charge duality in integrable lattice models
- On the completeness of solutions of Bethe's equations
- On Generalized Gibbs Ensembles with an infinite set of conserved charges
- Quantum relaxation and finite size effects in the XY chain in a transverse field after global quenches
- Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species
- Fast analytic solver of rational Bethe equations
- Exact solution for the quench dynamics of a nested integrable system
- Short distance correlators in the XXZ spin chain for arbitrary string distributions
- Functional Relations in Solvable Lattice Models II
- Integrable Matrix Product States from boundary integrability
- Applicability of the generalized Gibbs ensemble after a quench in the quantum Ising chain
- Excited state correlations of the finite Heisenberg chain
- Global large time dynamics and the generalized Gibbs ensemble
- Overlaps with arbitrary two-site states in the XXZ spin chain
- Discrete Hirota's equation in quantum integrable models
- Integrable quenches in nested spin chains I: the exact steady states
- Analytic theory of the eight-vertex model
- Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
- Correlation and entanglement spreading in nested spin chains
- The equilibrium landscape of the Heisenberg spin chain
- The generalized Gibbs ensemble as a pseudo-initial state: its predictive power revealed in a second quench
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