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Helvetica Physica Acta (Switzerland)

Local perturbations and limiting Gibbs states of quantum lattice mean-field systems

Thomas Gerisch

Published Oct 29, 1994• 3 citations
Publisher
DOI
10.5169/seals-116660

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Abstract We prove that the magnetization is equal to the edge current in the thermodynamic limit for a large class of models of lattice fermions with finite-range interactions satisfying local indistinguishability of the Gibbs state, a condition known to hold for sufficiently high temperatures. Our result implies that edge currents in such systems are determined by bulk properties and are therefore stable against large perturbations near the boundaries. Moreover, the equality persists also after taking the derivative with respect to the chemical potential. We show that this form of bulk-edge correspondence is essentially a consequence of homogeneity in the bulk and locality of the Gibbs state. An important intermediate result is a new version of Bloch’s theorem for two-dimensional systems, stating that persistent currents vanish in the bulk.
Integrable quantum many-body systems are considered to equilibrate to generalized Gibbs ensembles (GGEs). A general mechanism of such relaxation to GGE has been shown for unitary evolutions of exactly solvable quadratic bosonic systems in the thermodynamic limit. Here, we explore the role of locality and interaction with surroundings in the relaxation by considering the reduced dynamics of a class of open systems weakly interacting with a reservoir, which is initially prepared in a locally perturbed GGE. The standard derivation of a quantum master equation fails to describe relaxation to GGE in the long-time limit in the presence of the initial perturbation. We investigate a proper quantum master equation that guarantees the relaxation to GGE to avoid this counterintuitive issue and describes the relaxation to the reduced state corresponding to GGE in the thermodynamic limit. In particular, we show that the stationary state of the open system is fully characterized by GGE of the reservoir, which is independent of the initial local perturbation.