Quantum simulation of thermodynamics: Maxwell relations for pair correlations

TL;DR

This paper introduces generalized Maxwell relations that connect thermodynamic properties to local correlation functions, enabling easier thermodynamic characterization in quantum simulators and potentially advancing material science research.

Contribution

The paper develops generalized Maxwell relations linking thermodynamic quantities to local correlations, facilitating thermodynamic measurements in quantum simulators.

Findings

Derived universal Maxwell relations for quantum many-body models.

Demonstrated thermodynamic property deduction from pair correlations.

Suggested applications to challenging condensed matter systems.

Abstract

Quantum simulators hold enormous promise for advancing the modelling of materials and understanding emergent physics, such as high temperature superconductivity and topological order. While correlation functions are, typically, straightforward to measure in quantum simulators, thermodynamic properties are not. This limits our ability to directly compare the results of quantum simulations to experiments on the materials being modelled. Maxwell relations are an extremely powerful tool for characterising complex materials, as they enable the determination of challenging-to-measure thermodynamic properties from more accessible ones. Here, we introduce generalised Maxwell relations that relate every thermodynamic quantity to a single local correlation function. We illustrate their utility by deducing the thermodynamic properties of several iconic quantum many-body models from pair correlation functions using the generalised Maxwell relations. We show that this {universal} approach is readily accessible in quantum simulators and suggest applications to condensed matter systems where thermodynamic measurements are challenging, such as atomically thin materials.