Thermalization and pseudolocality in extended quantum systems

Abstract

Recently, it was understood that modified concepts of locality played an important role in the study of extended quantum systems out of equilibrium, in particular in so-called generalized Gibbs ensembles. In this paper, we rigorously study pseudolocal charges and their involvement in time evolutions and in the thermalization process of arbitrary states with strong enough clustering properties. We show that the densities of pseudolocal charges form a Hilbert space, with inner product determined by thermodynamic susceptibilities. Using this, we define the family of pseudolocal states, which are determined by pseudolocal charges. This family includes thermal Gibbs states at high enough temperatures, as well as (a precise definition of) generalized Gibbs ensembles. We prove that the family of pseudolocal states is preserved by finite time evolution, and that, under certain conditions, the stationary state emerging at infinite time is a generalized Gibbs ensemble with respect to the evolution dynamics. If the evolution dynamics does not admit any conserved pseudolocal charges other than the evolution Hamiltonian, we show that any stationary pseudolocal state with respect to this dynamics is a thermal Gibbs state, and that Gibbs thermalization occurs. The framework is that of translation-invariant states on hypercubic quantum lattices of any dimensionality (including quantum chains) and finite-range Hamiltonians, and does not involve integrability.

v1: 43 pages. v2: corrections and clarifications, references added, 46 pages. v3: 48 pages, further corrections made, accepted for publication in Commun. Math. Phys

References in corpus (27)

• Thermalization and its mechanism for generic isolated quantum systems
• Quantum Quench in the Transverse Field Ising Chain
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• 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
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• 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
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Generalized Gibbs Ensembles for Quantum Field Theories
• Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
• Quantum Quench from a Thermal Initial State
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• String-charge duality in integrable lattice models
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Exactly conserved quasilocal operators for the XXZ spin chain
• Equilibration via Gaussification in fermionic lattice systems
• Memory-preserving equilibration after a quantum quench in a 1d critical model
• Quasilocal conservation laws from semicyclic irreducible representations of $U_q({\mathfrak{sl}}_2)$ in $XXZ$ spin-$1/2$ chains
• Entropic Fluctuations in Quantum Statistical Mechanics. An Introduction
• Equilibration and GGE in interacting-to-free Quantum Quenches in dimensions d>1

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