Semiclassical Approach to Survival Probability at Quantum Phase Transitions

TL;DR

This paper develops a semiclassical theory to describe how survival probability decays near quantum phase transitions, predicting different decay behaviors based on system dimensionality, and verifies these predictions through numerical models.

Contribution

It introduces a semiclassical framework for understanding survival probability decay at quantum phase transitions, highlighting the role of system dimensionality.

Findings

Power law decay in 1D systems near critical points

Exponential decay in higher-dimensional systems

Numerical validation across four models

Abstract

We study the decay of survival probability at quantum phase transitions (QPT). The semiclassical theory is found applicable in the vicinities of critical points with infinite degeneracy. The theory predicts a power law decay of the survival probability for relatively long times in systems with d=1 and an exponential decay in systems with sufficiently large d, where d is the degrees of freedom of the underlying classical dynamics. The semiclassical predictions are checked numerically in four models.