Semiclassical approximation solved by Monte Carlo as an efficient impurity solver for dynamical mean field theory and its cluster extensions

TL;DR

This paper introduces a combined semiclassical and Monte Carlo method as an efficient impurity solver for dynamical mean field theory, accurately capturing main spectral features in complex models with large clusters.

Contribution

The paper presents a novel combination of semiclassical approximation with Monte Carlo simulations as an impurity solver for large-cluster dynamical mean field theory, demonstrating its reliability.

Findings

Reasonable estimates of the metal-insulator transition point

Main spectral features are well reproduced

Method is efficient for large cluster sizes

Abstract

We propose that a combination of the semiclassical approximation with Monte Carlo simulations can be an efficient and reliable impurity solver for dynamical mean field theory equations and their cluster extensions with large cluster sizes. In order to show the reliability of the method, we consider two test cases: (i) the single-band Hubbard model within the dynamical cluster approximation with 4- and 8-site clusters and (ii) the anisotropic two-orbital Hubbard model with orbitals of different band width within the single-site dynamical mean field theory. We compare our results with those obtained from solving the dynamical mean field equations with continuous time and determinant quantum Monte Carlo. In both test cases we observe reasonable values of the metal-insulator critical interaction strength $U_c/t$ and, while some details of the spectral functions cannot be captured by the semiclassical approximation due to the freezing of dynamical fluctuations, the main features are reproduced by the approach.