Quantum Statistical Physics of Glasses at Low Temperatures

TL;DR

This paper develops a quantum statistical model for low-temperature glasses, combining perturbative and non-perturbative methods, and validates results with Quantum Monte Carlo simulations, reproducing characteristic anomalies in specific heat.

Contribution

It introduces a microscopic mean-field quantum model for glasses at low temperatures and compares perturbative, static, and Monte Carlo methods for analyzing its properties.

Findings

Perturbative two-loop results agree with Quantum Monte Carlo simulations.

The model reproduces low-temperature specific heat anomalies.

Static approximation and perturbative methods yield consistent results.

Abstract

We present a quantum statistical analysis of a microscopic mean-field model of structural glasses at low temperatures. The model can be thought of as arising from a random Born von Karman expansion of the full interaction potential. The problem is reduced to a single-site theory formulated in terms of an imaginary-time path integral using replicas to deal with the disorder. We study the physical properties of the system in thermodynamic equilibrium and develop both perturbative and non-perturbative methods to solve the model. The perturbation theory is formulated as a loop expansion in terms of two-particle irreducible diagrams, and is carried to three-loop order in the effective action. The non-perturbative description is investigated in two ways, (i) using a static approximation, and (ii) via Quantum Monte Carlo simulations. Results for the Matsubara correlations at two-loop order perturbation theory are in good agreement with those of the Quantum Monte Carlo simulations. Characteristic low-temperature anomalies of the specific heat are reproduced, both in the non-perturbative static approximation, and from a three-loop perturbative evaluation of the free energy. In the latter case the result so far relies on using Matsubara correlations at two-loop order in the three-loop expressions for the free energy, as self-consistent Matsubara correlations at three-loop order are still unavailable. We propose to justify this by the good agreement of two-loop Matsubara correlations with those obtained non-perturbatively via Quantum Monte Carlo simulations.