We have studied the role of heat-bath coupling in a quantum spin glass described by a previously developed random-bond random-field Ising model in a transverse field, which accounts for quantum tunneling of protons in a disordered hydrogen-bonded ferroelectric. In contrast to the stochastic model considered earlier, it is assumed that proton tunneling is not directly affected by the thermal fluctuations and thus remains coherent. The basic mechanism that renders the system dissipative is heat-bath-assisted jumps of protons across the potential barrier. An effective single-spin Hamiltonian is obtained on the basis of a thermofield dynamic approach in the short-time limit. A resolvent expansion of the underlying time-evolution operator is then set up and the resulting resonance line shape calculated to leading order in the perturbation theory. It is shown that at low frequencies the line shape exhibits a singular contribution that diverges as ∼‖ω${\mathrm{\Vert }}^{\mathrm{-}1/2}$, but disappears in the classical limit of zero tunneling frequency. This singularity is due to coherent tunneling motion and is thus a typical quantum effect which could be observed in the NMR, NQR, or EPR line shapes in the appropriate temperature range.

• Received 9 September 1992

DOI:https://doi.org/10.1103/PhysRevB.47.8801