Statistical mechanics of quantum spin systems. II
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.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- December 1968
- DOI:
- 10.1007/BF01646665
- Bibcode:
- 1968CMaPh...7..337R
- Keywords:
-
- Boundary Condition;
- Neural Network;
- Statistical Physic;
- Equilibrium State;
- Complex System