Sherrington-Kirkpatrick model in a transverse field: Absence of replica symmetry breaking due to quantum fluctuations

The Sherrington-Kirkpatrick model under a transverse field is studied here employing the Suzuki-Trotter formula to map the model to an equivalent classical one. The effective Thouless-Anderson-Palmer free energy is used to study the stability of the system, and Monte Carlo computer simulations of the effective classical model are performed to obtain the phase diagram and the magnetization overlap distribution. Our results indicate a trivial overlap distribution due to quantum fluctuations. The phase diagram shows a slight initial increase in the glass transition temperature $T_g$ as the transverse field is switched on, confirming that obtained by Yokota.