Relaxation in quantum spin glasses

Abstract

The dynamics of a quantum spin glass, which is described by the random-bond-random-field Ising model in a transverse field, Ω, and is in contact with a heat bath, are studied. The model is applicable to disordered hydrogen bonded ferroelectrics with Ω representing the tunneling frequency of the protons. A special type of heat-bath coupling is considered where proton tunneling is modulated by the thermal fluctuations but remains coherent. The underlying time evolution operator is obtained by means of the resolvent expansion method. The long-time dependence of the polarization, P +( t), after switching off a uniform field is shown to follow a power-law behavior, which is a quantum effect.