Session S30 - Mathematical Methods in Quantum Mechanics

Monday, July 19, 18:30 ~ 18:55 UTC-3

On the Equivalence of the KMS Condition and the Variational Principle for Quantum Lattice Systems with Mean-Field Interactions

Walter de Siqueira Pedra

University of São Paulo, Brazil   -   wpedra@if.usp.br

We extended Araki's result on the equivalence of the KMS condition and the variational principle for equilibrium states of quantum lattice systems with short-range interactions, to a large class of lattice models possibly containing mean-field interactions (representing an extreme form of long-range interactions). This result is reminiscent of van Hemmen's work on equilibrium states for mean-field models. The extension was made possible by our recent outcomes on states minimizing the free energy density of mean-field models on the lattice, as well as on the infinite volume dynamics for such models.

Joint work with Jean-Bernard Bru (Ikerbasque and BCAM, Spain) and Rafael Sussumu Yamaguti Miada (University of São Paulo, Brazil).

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