Cluster Perturbation Theory for Hubbard models

TL;DR

Cluster perturbation theory is a versatile method for approximating the spectral functions of Hubbard models, accurately capturing both strong and weak coupling regimes by combining exact cluster solutions with perturbation theory.

Contribution

This paper provides a comprehensive description and derivation of cluster perturbation theory, extending its application to various properties and doping effects in Hubbard models.

Findings

Accurately models spectral weight across coupling regimes

Calculates ground state energy and double occupancy effectively

Shows disappearance of Fermi surface in doped Hubbard models

Abstract

Cluster perturbation theory is a technique for calculating the spectral weight of Hubbard models of strongly correlated electrons, which combines exact diagonalizations on small clusters with strong-coupling perturbation theory at leading order. It is exact in both the strong- and weak-coupling limits and provides a good approximation to the spectral function at any wavevector. Following the paper by S\'en\'echal et al. (Phys. Rev. Lett. {\bf 84}, 522 (2000)), we provide a more complete description and derivation of the method. We illustrate some of its capabilities, in particular regarding the effect of doping, the calculation of ground state energy and double occupancy, the disappearance of the Fermi surface in the $t-t'$ Hubbard model, and so on. The method is applicable to any model with on-site repulsion only.