Variational Cluster Approximation to the Thermodynamics of Quantum Spin Systems

TL;DR

This paper introduces a variational cluster approximation method for quantum Heisenberg spin systems at finite temperature, enabling the calculation of thermodynamic properties through a cluster-based variational approach inspired by self-energy functional theory.

Contribution

It develops a novel variational cluster approximation framework for quantum spin systems, extending ideas from fermionic and bosonic models to spin models, with explicit evaluation techniques.

Findings

Accurately reproduces thermodynamics of spin chains for various cluster sizes.

Shows good agreement with exact Bethe ansatz solutions.

Highlights potential limitations and technical considerations of the method.

Abstract

We derive a variational cluster approximation for Heisenberg spin systems at finite temperature based on the ideas of the self-energy functional theory by Potthoff for fermionic and bosonic systems with local interactions. Partitioning the real system into a set of clusters, we find an analytical expression for the auxiliary free energy, depending on a set of variational parameters defined on the cluster, whose stationary points provide approximate solutions from which the thermodynamics of spin models can be obtained. We explicitly describe the technical details of how to evaluate the free energy for finite clusters and remark on specific problems and possible limitations of the method. To test the approximation we apply it to the antiferromagnetic spin 1/2 chain and compare the results for varying cluster sizes and choices of variational parameters with the exact Bethe ansatz solution.