Quantum statistical physics of glasses at low temperatures

J. van Baardewijk, R. Kuehn

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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 nonperturbative 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 nonperturbative 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 nonperturbative 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 nonperturbatively via quantum Monte Carlo simulations.
Original languageEnglish
Article number054203
JournalPhysical Review B
Volume81
Issue number5
Publication statusPublished - 2 Feb 2010

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