Real-time non-equilibrium dynamics of quantum glassy systems

TL;DR

This paper develops an analytic framework to study the real-time aging dynamics of quantum glassy systems, revealing how quantum fluctuations influence phase transitions and aging behavior.

Contribution

It introduces a systematic approach combining path integrals and disorder averaging to analyze quantum glass dynamics, including quantum effects on phase transitions and aging.

Findings

Quantum fluctuations lower the spin-glass transition temperature.

A quantum critical point separates paramagnetic and spin-glass phases.

Aging persists in the quantum glassy phase, with modified fluctuation-dissipation relations.

Abstract

We develop a systematic analytic approach to aging effects in quantum disordered systems in contact with an environment. Within the closed-time path-integral formalism we include dissipation by coupling the system to a set of independent harmonic oscillators that mimic a quantum thermal bath. After integrating over the bath variables and averaging over disorder we obtain an effective action that determines the real-time dynamics of the system. The classical limit yields the Martin-Siggia-Rose generating functional associated to a colored noise. We apply this general formalism to a prototype model related to the $p$ spin-glass. We show that the model has a dynamic phase transition separating the paramagnetic from the spin-glass phase and that quantum fluctuations depress the transition temperature until a quantum critical point is reached. We show that the dynamics in the paramagnetic phase is stationary but presents an interesting crossover from a region controlled by the classical critical point to another one controlled by the quantum critical point. The most characteristic property of the dynamics in a glassy phase, namely aging, survives the quantum fluctuations. In the sub-critical region the quantum fluctuation-dissipation theorem is modified in a way that is consistent with the notion of effective temperatures introduced for the classical case. We discuss these results in connection with recent experiments in dipolar quantum spin-glasses and the relevance of the effective temperatures with respect to the understanding of the low temperature dynamics.