Exact Solution for the Transverse Field Sherrington-Kirkpatrick Spin Glass Model with Continuous-Time Quantum Monte Carlo Method

We construct the first complete exact numerical solution of a mean field quantum spin glass model, the transverse field Sherrington-Kirkpatrick model, by implementing a continuous-time quantum Monte Carlo method in the presence of full replica symmetry breaking. We extract the full numerically exact phase diagram, displaying a glassy phase with continuous replica symmetry breaking at small transverse fields and low temperatures. A paramagnetic phase emerges once thermal and quantum fluctuations melt the spin glass. We characterize both phases by extracting the order parameter, as well as the static and dynamical local spin susceptibilities. The static susceptibility shows a plateau in the glassy phase, but remains smooth across the phase boundary, while the shape of dynamical susceptibility varies upon crossing the glass transition by reducing quantum fluctuations. We qualitatively compare these results to a.c. susceptibility measurements on dipole-coupled Ising magnets in a transverse magnetic field. Our work provides a general framework for the exact numerical solution of mean field quantum glass models, constituting an important step towards understanding glassiness in realistic systems.