Quantum Monte Carlo Study of Strongly Correlated Electrons: Cellular Dynamical Mean-Field Theory

TL;DR

This paper applies Cellular Dynamical Mean-Field Theory combined with Quantum Monte Carlo simulations to study the Hubbard model, providing insights into the method's performance and cluster size effects in strongly correlated electron systems.

Contribution

It details the implementation of CDMFT with QMC for the Hubbard model and evaluates its accuracy against exact results and other methods for small clusters.

Findings

CDMFT+QMC accurately reproduces known results for small clusters.

Cluster size significantly affects Green's functions and self-energies.

Method performance varies between one- and two-dimensional systems.

Abstract

We study the Hubbard model using the Cellular Dynamical Mean-Field Theory (CDMFT) with quantum Monte Carlo (QMC) simulations. We present the algorithmic details of CDMFT with the Hirsch-Fye QMC method for the solution of the self-consistently embedded quantum cluster problem. We use the one- and two-dimensional half-filled Hubbard model to gauge the performance of CDMFT+QMC particularly for small clusters by comparing with the exact results and also with other quantum cluster methods. We calculate single-particle Green's functions and self-energies on small clusters to study their size dependence in one- and two-dimensions.