Off-Diagonal Series Expansion for Quantum Partition Functions

TL;DR

This paper introduces an off-diagonal series expansion method for quantum partition functions, allowing analytical calculations of thermodynamic properties in quantum systems by expanding around classical parts.

Contribution

It presents a novel integral-free perturbation series expansion for quantum partition functions, enabling analytical term-by-term calculations around classical Hamiltonian components.

Findings

Analytical third-order partition functions for 1D Ising model with fields

Partition functions computed for quantum 1D Heisenberg model

Method simplifies quantum thermodynamic calculations

Abstract

We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the classical component of the Hamiltonian with the expansion parameter being the strength of the off-diagonal, or quantum, portion. To demonstrate the usefulness of the technique we analytically compute to third order the partition functions of the 1D Ising model with longitudinal and transverse fields, and the quantum 1D Heisenberg model.