Model calculation for the susceptibility of a quantum spin glass

Abstract

We have studied the dynamic susceptibility in a quantum spin glass which is described by an Ising model in a transverse field, the latter introducing quantum tunneling in an otherwise classical problem. An effective single-spin Hamiltonian is obtained on the basis of an extant thermofield dynamic approach. The coupling to a dissipative heat bath is designed to affect thermal as well as quantal fluctuations and to yield Glauber kinetics in the absence of the transverse field. A resolvent expansion of the underlying time-development operator is then set up and the dynamic susceptibility calculated to leading order in perturbation theory. It is shown that the frequency of the peak of the susceptibility shifts towards higher values of ω , its amplitude is reduced and peaks are broadened as quantum effects strengthen. Our results are in qualitative agreement with the experimentally studied crystal-field-split system of LiHo_xY_1-xF₄ by Wu et al.