Specific Heat of Quantum Elastic Systems Pinned by Disorder

TL;DR

This paper investigates the low-temperature specific heat of disordered elastic systems, revealing a cubic temperature dependence in 2D and 3D, with the prefactor influenced by pinning length, using a mean field quantum approach.

Contribution

It provides a detailed quantum thermodynamic analysis of disordered elastic systems, deriving the specific heat behavior and its dependence on disorder and dimensionality.

Findings

Specific heat scales as T^3 at low temperatures in 2D and 3D.

Cancellation of linear T term in specific heat calculation.

Pinning length controls the prefactor of the specific heat.

Abstract

We present the detailed study of the thermodynamics of vibrational modes in disordered elastic systems such as the Bragg glass phase of lattices pinned by quenched impurities. Our study and our results are valid within the (mean field) replica Gaussian variational method. We obtain an expression for the internal energy in the quantum regime as a function of the saddle point solution, which is then expanded in powers of $\hbar$ at low temperature $T$. In the calculation of the specific heat $C_v$ a non trivial cancellation of the term linear in $T$ occurs, explicitly checked to second order in $\hbar$. The final result is $C_v \propto T^3$ at low temperatures in dimension three and two. The prefactor is controlled by the pinning length. This result is discussed in connection with other analytical or numerical studies.