Finite and High-temperature series expansion via many-body perturbation theory

TL;DR

This paper introduces a new algorithm for calculating finite and high-temperature series expansions of the grand potential using many-body perturbation theory, demonstrated on the Heisenberg spin-1/2 XXZ chain.

Contribution

The paper presents a novel algorithm that formulates each order as a divided difference, enabling efficient high-temperature series expansion calculations.

Findings

Coefficients of the high-temperature expansion up to sixth order obtained

Applied the algorithm to the Heisenberg spin-1/2 XXZ chain

Demonstrated the effectiveness of the method for thermodynamic quantities

Abstract

We present a new algorithm to evaluate the grand potential at finite and high-temperature series expansion via many-body perturbation theory. This algorithm allows us to formulate each order as a divided difference. Further, we apply this algorithm to the Heisenberg spin-1/2 XXZ chain. We obtain all coefficients of the high-temperature expansion of the free energy and susceptibility per site of this model up to sixth order.