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Statistical mechanics of quantum spin systems. II

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Abstract

In the first part of this paper we continue the general analysis of quantum spin systems. It is demonstrated, for a large class of interactions, that time-translations form a group of automorphisms of theC*-algebra\(\mathfrak{A}\) of quasi-local observables and that the thermodynamic equilibrium states are invariant under this group. Further it is shown that the equilibrium states possess the Kubo-Martin-Schwinger analyticity and boundary condition properties. In the second part of the paper we give a general analysis of states which are invariant under space and time translations and also satisfy the KMS boundary condition. A discussion of these latter conditions and their connection with the decomposition of invariant states into ergodic states is given. Various properties pertinent to this discussion are derived.

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Supported in part by the Office of Naval Research Contract No. Nonr 1866 (5).

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Robinson, D.W. Statistical mechanics of quantum spin systems. II. Commun.Math. Phys. 7, 337–348 (1968). https://doi.org/10.1007/BF01646665

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  • DOI: https://doi.org/10.1007/BF01646665

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