A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I

We introduce a class of gapped Hamiltonians on quantum spin chains, which allows asymmetric edge ground states. This class is an asymmetric generalization of the class of Hamiltonians in [FNS]. It can be characterized by five qualitative physical properties of ground state structures. In this Part I, we introduce the models and investigate their properties.Comment: Final versio

The Shannon-McMillan Theorem for AF C∗C^*-systems

We give a new proof of quantum Shannon-McMillan theorem, extending it to AF $C^*$-systems. Our proof is based on the variational principle, instead of the classical Shannon-McMillan theorem

Ruelle-Lanford functions for quantum spin systems

We prove a large deviation principle for the expectation of macroscopic observables in quantum (and classical) Gibbs states. Our proof is based on Ruelle-Lanford functions and direct subadditivity arguments, as in the classical case, instead of relying on G\"artner-Ellis theorem, and cluster expansion or transfer operators as done in the quantum case. In this approach we recover, expand, and unify quantum (and classical) large deviation results for lattice Gibbs states. In the companion paper \cite{OR} we discuss the characterization of rate functions in terms of relative entropies.Comment: 22 page