Dobrushin States in Quantum Lattice Systems

We consider quantum lattice systems which are quantum perturbations of suitable classical systems with two translation-invariant ground states, not necessarily related by symmetry. Simple examples of such systems include the anisotropic quantum Heisenberg model and the narrow band extended Hubbard model. Under the assumption that the quantum perturbation is exponentially decaying with a sufficiently large decay constant, we prove that these systems are capable of supporting non-translation-invariant states at sufficiently low temperatures in dimension . These states are induced by so-called Dobrushin boundary conditions which force an asymptotically horizontal interface into the system. We also discuss quantum and classical interfacial ordering transitions that may occur in these systems. Received: 15 October 1996 / Accepted: 21 February 1997