Low temperature relaxational dynamics of the Ising chain in a transverse field

TL;DR

This paper provides exact low-temperature real-time correlation results for the 1D Ising model in a transverse field, combining quantum and classical effects, and confirms predictions with numerical simulations.

Contribution

It offers asymptotically exact analytical expressions for correlations in the 1D transverse field Ising model at low temperatures, bridging quantum and classical dynamics.

Findings

Correlation functions factor into quantum and classical parts.

Predictions match numerical simulations without free parameters.

Results clarify relaxational dynamics near quantum criticality.

Abstract

We present asymptotically exact results for the real time order parameter correlations of a class of d=1 Ising models in a transverse field at low temperatures (T) on both sides of the quantum critical point. The correlations are a product of a T-independent factor determined by quantum effects, and a T-dependent relaxation function which comes from a classical theory. We confirm our predictions by a no-free-parameter comparison with numerical studies on the nearest neighbor spin-1/2 model.