Large deviations for quantum spin probabilities at temperature zero

Abstract

We consider certain self-adjoint observable for the KMS state associated to the Hamiltonian [Formula: see text] over the quantum spin lattice [Formula: see text]. For a fixed observable of the form [Formula: see text], where [Formula: see text], and for the zero temperature limit one can get a naturally defined stationary probability [Formula: see text] on the Bernoulli space [Formula: see text]. This probability is ergodic but it is not mixing for the shift map. It is not a Gibbs state for a continuous normalized potential but its Jacobian assume only two values almost everywhere. Anyway, for such probability [Formula: see text] we can show that a Large Deviation Principle is true for a certain class of functions. The result is derived by showing the explicit form of the free energy which is differentiable.