Boundary conditions for quantum lattice systems
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.
Keywords
Cite
@article{arxiv.cond-mat/9504090,
title = {Boundary conditions for quantum lattice systems},
author = {M. Fannes and R. F. Werner},
journal= {arXiv preprint arXiv:cond-mat/9504090},
year = {2007}
}
Comments
plain TeX, 26 pages, 5 figures in separate compressed .ps file. full postscript version from: ftp://ftp.physik.uni-osnabrueck.de/pub/werner/BoundaryConds/bcq.ps