A Maximum Entropy Method of Obtaining Thermodynamic Properties from Quantum Monte Carlo Simulations

TL;DR

This paper introduces a Bayesian Maximum Entropy method to extract thermodynamic properties from Quantum Monte Carlo data without assuming specific functional forms, enabling accurate calculations of energy, entropy, and specific heat.

Contribution

The paper presents a novel, assumption-free Bayesian Maximum Entropy approach to derive thermodynamic properties from quantum simulation data, incorporating prior information effectively.

Findings

Successfully applied to the 3D Periodic Anderson Model

Accurately computes specific heat and entropy with error bars

No need for predefined functional forms of energy

Abstract

We describe a novel method to obtain thermodynamic properties of quantum systems using Baysian Inference -- Maximum Entropy techniques. The method is applicable to energy values sampled at a discrete set of temperatures from Quantum Monte Carlo Simulations. The internal energy and the specific heat of the system are easily obtained as are errorbars on these quantities. The entropy and the free energy are also obtainable. No assumptions as to the specific functional form of the energy are made. The use of a priori information, such as a sum rule on the entropy, is built into the method. As a non-trivial example of the method, we obtain the specific heat of the three-dimensional Periodic Anderson Model.