The spectral weight of the Hubbard model through cluster perturbation theory

TL;DR

This paper uses cluster perturbation theory with exact diagonalizations of finite clusters to accurately compute the spectral weight of one- and two-dimensional Hubbard models, revealing key physical phenomena like spin-charge separation.

Contribution

It introduces a method combining exact diagonalization and perturbation theory to efficiently approximate spectral weights in Hubbard models with modest cluster sizes.

Findings

Accurate spectral weight calculations with small clusters

Clear identification of spin-charge separation in 1D Hubbard model

Observation of extended spectral weight in 2D Hubbard model

Abstract

We calculate the spectral weight of the one- and two-dimensional Hubbard models, by performing exact diagonalizations of finite clusters and treating inter-cluster hopping with perturbation theory. Even with relatively modest clusters (e.g. 12 sites), the spectra thus obtained give an accurate description of the exact results. Thus, spin-charge separation (i.e. an extended spectral weight bounded by singularities) is clearly recognized in the one-dimensional Hubbard model, and so is extended spectral weight in the two-dimensional Hubbard model.