Quantum effects in rotationally invariant spin glass models.

Abstract

This study investigates the quantum effects in transverse-field Ising spin glass models with rotationally invariant random interactions. The primary aim is to evaluate the validity of a quasistatic approach that captures the imaginary-time dependence of the order parameters beyond the conventional static approximation. Using the replica method combined with the Suzuki-Trotter decomposition, we established a stability condition for the replica symmetric solution, which is analogous to the de Almeida-Thouless criterion. Numerical analysis of the Sherrington-Kirkpatrick model estimates a value of the critical transverse field, Γ_{c}, which is consistent with previous Monte Carlo-based estimations. For the Hopfield model, it provides an estimate of Γ_{c}, which has not been previously evaluated. For the random orthogonal model, our analysis suggests that quantum effects alter the random first-order transition scenario in the low-temperature limit. This study supports a quasistatic treatment for analyzing quantum spin glasses and may offer useful insights into the analysis of quantum optimization algorithms.