Variational cluster approach to spontaneous symmetry breaking: The itinerant antiferromagnet in two dimensions

TL;DR

This paper extends the cluster-perturbation theory within the self-energy-functional approach to effectively describe spontaneous symmetry breaking, combining short-range correlations with long-range order, and applies it successfully to the antiferromagnetic phase of the Hubbard model.

Contribution

The authors develop a variational extension of cluster-perturbation theory that accurately captures both short-range correlations and long-range magnetic order in models with local interactions.

Findings

Good agreement with quantum Monte-Carlo results for the Hubbard model.

The method effectively reproduces key features of the single-particle spectrum.

It offers a more flexible and less computationally demanding approach at zero temperature.

Abstract

Based on the self-energy-functional approach proposed recently [M. Potthoff, Eur. Phys. J. B 32, 429 (2003)], we present an extension of the cluster-perturbation theory to systems with spontaneously broken symmetry. Our method applies to models with local interactions and accounts for both short-range correlations and long-range order. Short-range correlations are accurately taken into account via exact diagonalization of finite clusters. Long-range order is described by variational optimization of a ficticious symmetry-breaking field. In comparison with related cluster methods, our approach is more flexible and, for a given cluster size, less demanding numerically, especially at zero temperature. An application of the method to the antiferromagnetic phase of the Hubbard model at half-filling shows good agreement with results from quantum Monte-Carlo calculations. We demonstrate that the variational extension of the cluster-perturbation theory is crucial to reproduce salient features of the single-particle spectrum.