127 research outputs found
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 -systems
We give a new proof of quantum Shannon-McMillan theorem, extending it to AF
-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
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