Applicability and limitations of cluster perturbation theory for Hubbard models

TL;DR

This paper examines the use of Cluster Perturbation Theory (CPT) for Hubbard models, highlighting its applications and limitations, especially regarding spectral resolution and the study of metal-insulator transitions.

Contribution

It provides a detailed analysis of CPT's applicability to Hubbard models and discusses the limitations imposed by finite cluster sizes in spectral and transition studies.

Findings

CPT effectively models spectral functions for small clusters.

Finite-size effects limit the resolution of spectral features.

Large clusters are needed to accurately study the metal-insulator transition.

Abstract

We present important use cases and limitations when considering results obtained from Cluster Perturbation Theory (CPT). CPT combines the solutions of small individual clusters of an infinite lattice system with the Bloch theory of conventional band theory in order to provide an approximation for the Green's function in the thermodynamic limit. To this end we are investigating single-band and multi-band Hubbard models in one- and two-dimensional systems. A special interest is taken in the supposed pseudo gap regime of the two-dimensional square lattice at half filling and intermediate interaction strength ($U \leq 3t$) as well as the metal-insulator transition. We point out that the finite-size level spacing of the cluster limits the resolution of spectral features within CPT. This restricts the investigation of asymptotic properties of the metal-insulator transition, as it would require much larger cluster sizes that are beyond computational capabilities.