Dynamical correlations in the Sherrington-Kirkpatrick model in a transverse field

TL;DR

This paper analyzes the real-time correlations in the quantum spin-glass model, revealing power-law decay behaviors at different temperature regimes and field strengths, advancing understanding of quantum spin dynamics.

Contribution

It provides a detailed calculation of the correlation function in the SK model with a transverse field, highlighting new decay behaviors and phase-dependent structural differences.

Findings

Power-law decay of correlations as t^{-3/2} at zero temperature for large fields

Power-law decay of correlations as t^{-2} at infinite temperature

Significant correlation changes at small fields due to phase differences

Abstract

We calculate the real-time-correlation function of the Sherrington-Kirkpatrick spin-glass model in a transverse field. Using a careful analysis of the perturbative expansion of the functional-integral representation, we derive the asymptotic form of the correlation function. In contrast to the previous works, we find for large transverse field a power-law decay of the correlation with time $t$ as $t^{-3/2}$ at zero temperature and $t^{-2}$ at infinite temperature. At the small field region, we also find a significant change in the correlation which comes from the structural difference between two paramagnetic phases.