2015/12/31 by Benjamin Doyon · 5 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Canonical ensemble #Gibbs state #Hamiltonian (control theory) #Hilbert space #Mathematics #Ministate #Opinion Dynamics and Social Influence #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Statistical physics #Thermalisation #Time evolution #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/s00220-017-2836-7
published as Commun. Math. Phys. 351: 155-200 (2017) · v1: 43 pages. v2: corrections and clarifications, references added, 46 pages. v3: 48 pages, further corrections made, accepted for publication in Commun. Math. Phys
arxiv created 2016/12/18 · openalex publication_date 2017/02/09 · arxiv updated 2018/10/23 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
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.