Benchmarking a semiclassical impurity solver for dynamical-mean-field theory: self-energies and magnetic transitions of the single-orbital Hubbard model

TL;DR

This paper evaluates a semiclassical impurity solver for dynamical-mean-field theory, demonstrating its effectiveness in approximating self-energies and magnetic transitions in the single-orbital Hubbard model with reasonable accuracy and lower computational cost.

Contribution

It introduces a semiclassical approximation method for quantum-impurity problems in DMFT and validates its accuracy against quantum Monte-Carlo and exact diagonalization results.

Findings

Semiclassical method yields self-energies close to quantum Monte-Carlo results.

Accurately predicts magnetic transition temperatures across various parameters.

Offers a computationally cheaper alternative for studying correlated-electron models.

Abstract

An investigation is presented of the utility of semiclassical approximations for solving the quantum-impurity problems arising in the dynamical-mean-field approach to the correlated-electron models. The method is based on performing a exact numerical integral over the zero-Matsubara-frequency component of the spin part of a continuous Hubbard-Stratonovich field, along with a spin-field-dependent steepest descents treatment of the charge part. We test this method by applying it to one or two site approximations to the single band Hubbard model with different band structures, and comparing the results to quantum Monte-Carlo and simplified exact diagonalization calculations. The resulting electron self-energies, densities of states and magnetic transition temperatures show reasonable agreement with the quantum Monte-Carlo simulation over wide parameter ranges, suggesting that the semiclassical method is useful for obtaining a reasonable picture of the physics in situations where other techniques are too expensive.