Boundary conditions for quantum lattice systems

authored by

M. Fannes, R. F. Werner

Abstract

For classical lattice systems, the Dobrushin-Lanford-Ruelle theory of boundary conditions states that the restriction of a global equilibrium state to a subsystem can be obtained as an integral over equilibrium states of the subsystem alone. The Hamiltonians for the subsystem are obtained by fixing a configuration for the variables in the complement of the subsystem, or more generally, by evaluating the full interaction Hamiltonian with respect to a state for the complement. We provide examples showing that the quantum mechanical version of this statement is false. It fails even if the subsystem is classical, but embedded into a quantum environment. We suggest an alternative characterization of the local restrictions of global equilibrium states by inequalities involving only local data.

Organisation(s)

Institute of Theoretical Physics

External Organisation(s)

KU Leuven

Type

Article

Journal

Helv. Phys. Acta

Volume

68

Pages

635-657

No. of pages

23

Publication date

1995

Publication status

Published

Peer reviewed

Yes