Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering

Abstract

It has recently been shown that some integrable spin chains possess a set of quasilocal conserved charges, with the classic example being the spin-$\frac{1}{2}$ XXZ Heisenberg chain. These charges have been proven to be essential for properly describing stationary states after a quantum quench, and must be included in the generalized Gibbs ensemble (GGE). We find that similar charges are also necessary for the GGE description of integrable quantum field theories with non-diagonal scattering. A stationary state in a non-diagonal scattering theory is completely specified by fixing the mode-ocuppation density distributions of physical particles, as well auxiliary particles which carry no energy or momentum. We show that the set of conserved charges with integer Lorentz spin, related to the integrability of the model, are unable to fix the distributions of these auxiliary particles, since these charges can only fix kinematical properties of physical particles. The field theory analogs of quasilocal lattice charges are therefore necessary. As a concrete example, we find the complete set of charges needed in the sine-Gordon model, by using the fact that this field theory is recovered as the continuum limit of a spatially inhomogeneous version of the XXZ chain. The set of quasilocal charges of the lattice theory are shown to become a set local charges with fractional spin in the field theory.

arXiv commentv1: 30 pages, 4 figures v2: 35 pages, 5 figures; reorganization of the manuscript's structure, some discussions and references added

References in corpus (78)

• Many-Body Physics with Ultracold Gases
• 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
• Time-dependence of correlation functions following a quantum quench
• Quantum thermalization through entanglement in an isolated many-body system
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Light-cone-like spreading of correlations in a quantum many-body system
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Quantum Quench in the Transverse Field Ising Chain
• Generalized Gibbs ensemble in integrable lattice models
• Experimental Observation of a Generalized Gibbs Ensemble
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Time evolution of local observables after quenching to an integrable model
• The Luttinger model following a sudden interaction switch-on
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Microscopic observation of magnon bound states and their dynamics
• Local emergence of thermal correlations in an isolated quantum many-body system
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Dephasing and the steady state in quantum many-particle systems
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Reduced Density Matrix after a Quantum Quench
• Solution for an interaction quench in the Lieb-Liniger Bose gas
• Families of quasi-local conservation laws and quantum spin transport
• Quantum quench in an atomic one-dimensional Ising chain
• Quantum Quenches in Integrable Field Theories
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
• A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Analytic results for a quantum quench from free to hard-core one dimensional bosons
• Generalized Gibbs Ensembles for Quantum Field Theories
• Equilibration of a Tonks-Girardeau gas following a trap release
• Quantum quench in interacting field theory: a self-consistent approximation
• Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
• Quantum quench in the sine-Gordon model
• Infinite-time Average of Local Fields in an Integrable Quantum Field Theory after a Quantum Quench
• Quantum Quench from a Thermal Initial State
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• Dynkin TBA's
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Non linear integral equation and excited--states scaling functions in the sine-Gordon model
• Multi-particle bound state formation following a quantum quench to the one-dimensional Bose gas with attractive interactions
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• Nonlinear Integral Equation and Finite Volume Spectrum of Sine-Gordon Theory
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Spectroscopy of Collective Excitations in Interacting Low-Dimensional Many-Body Systems Using Quench Dynamics
• Non-equilibrium steady states in the Klein-Gordon theory
• Exactly conserved quasilocal operators for the XXZ spin chain
• Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories
• Quantum quenches in the sinh-Gordon model: steady state and one point correlation functions
• Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics
• Quantum quenches in the sine--Gordon model: a semiclassical approach
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Quasilocal conservation laws from semicyclic irreducible representations of $U_q({\mathfrak{sl}}_2)$ in $XXZ$ spin-$1/2$ chains
• Quasi-local conserved charges and spin transport in spin-$1$ integrable chains
• Lattice regularization of massive and massless integrable field theories
• Interaction quench in a trapped one-dimensional Bose gas
• The quench action approach in finite integrable spin chains
• Bethe Ansatz and Quantum Groups: The Light--Cone Approach. II. From RSOS($p+1$) models to $p-$restricted Sine--Gordon Field Theories
• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• Sine-Gordon form factors in finite volume
• Thermodynamic Bethe ansatz for non-equilibrium steady states: exact energy current and fluctuations in integrable QFT
• Real-time dynamics in a strongly interacting bosonic hopping model: Global quenches and mapping to the XX chain
• Stationary state after a quench to the Lieb-Liniger from rotating BECs
• Lectures on Integrable Structures in Quantum Field Theory and Massive ODE/IM Correspondence
• Equilibration and GGE for hard wall boundary conditions
• Chiral Prethermalization in supersonically split condensates
• TBA equations for excited states in the Sine-Gordon model
• The continuum limit of $a_{N-1}^{(2)}$ spin chains
• Discrete holomorphicity and quantized affine algebras

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• On Generalized Gibbs Ensembles with an infinite set of conserved charges
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
• Entanglement spreading in non-equilibrium integrable systems
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Rényi entropies after releasing the Néel state in the XXZ spin-chain
• Exact solution for the quench dynamics of a nested integrable system
• Entanglement revivals as a probe of scrambling in finite quantum systems
• Integrability-protected adiabatic reversibility in quantum spin chains
• Generalized Eigenstate Thermalization in 2d CFTs
• Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
• Rényi entropies of generic thermodynamic macrostates in integrable systems
• Non-Equilibrium Steady State generated by a moving defect: the supersonic threshold
• Quasi-local charges and the Generalized Gibbs Ensemble in the Lieb-Liniger model
• Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density
• Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
• Diffusive Hydrodynamics of Inhomogenous Hamiltonians
• Quantum quench in the attractive regime of the sine-Gordon model
• Loschmidt Amplitude and Work Distribution in Quenches of the Sine-Gordon Model
• Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas
• Probing non-thermal density fluctuations in the one-dimensional Bose gas
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• Superluminal moving defects in the Ising spin chain
• Lack of thermalization for integrability-breaking impurities
• The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
• Quenches from gaussian bosons to Tonks-Girardeau gas: stationary states and effects of a confining potential
• Popcorn Drude weights from quantum symmetry
• Quasilocal Conservation Laws in the Quantum Hirota Model
• Anomalous charge transport in the sine-Gordon model
• Integrable Floquet QFT: Elasticity and factorization under periodic driving
• Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench