Decay of Correlations for Quantum Spin Systems with a Transverse Field: A Dynamic Approach

We consider a wide class of quantum spin systems obtained by adding a transverse field to a classical Hamiltonian. We give explicit high-temperature conditions which guarantee exponential decay of correlations. A stochastic-geometric representation allows to reformulate the model as a classical random field on a space of marked point processes on the circle $[0,\beta)$, where $\beta$ is the inverse temperature. We then construct a Markov process having this random field as invariant measure. By the mixing properties of the process, the exponential decay of correlations follows by an adaptation of a general argument.