Observing quantum phase transitions at non-zero temperature: non-analytic behavior of order-parameter correlation times

TL;DR

This paper demonstrates that order-parameter correlation times in quantum many-body systems can exhibit non-analytic behavior at non-zero temperatures, revealing persistent quantum effects in local observable dynamics.

Contribution

It introduces a method to evaluate order-parameter correlation times at non-zero temperature, showing non-analytic behaviors indicative of quantum phase transitions in the dynamics.

Findings

Non-analytic behavior of spin correlation times as functions of magnetic field, velocity, and temperature.

Persistence of quantum fluctuation effects within local observable dynamics at finite temperature.

Logarithmic divergence in correlation times near the zero-temperature transition point.

Abstract

Phase transitions occur when a macroscopic number of local degrees of freedom coherently change their behavior. In ground states of quantum many-body systems, phase transitions due to quantum fluctuations are observed as non-analytic behaviors of order parameters, such as magnetization, as functions of a conjugate parameter, such as the magnetic field. However, as soon as thermal fluctuations are present, these effects are believed to disappear for local observables. We show that this is not necessarily the case: order parameters may still show non-analytic behaviors within their dynamics. With the example of the Ising model and using methods based on hydrodynamic fluctuations, we evaluate the exact order-parameter correlation time, in space-time directions of all velocities, in equilibrium states at nonzero temperature. We reveal non-analytic behaviors of spin correlation times as functions of the magnetic field, velocity, and temperature. As a function of the magnetic field, they occur at values that continuously approach that of the zero-temperature equilibrium transition point as the velocity is decreased and reach it within the light cone, where we obtain a new, temperature-independent logarithmic divergence characterizing the collective dynamics. Thus, collective effects induced by quantum fluctuations persist within the dynamics of local observables.