Cluster solver for dynamical mean-field theory with linear scaling in inverse temperature

TL;DR

This paper introduces a new determinant quantum Monte Carlo method for cluster solvers in dynamical mean-field theory that scales linearly with inverse temperature, significantly improving low-temperature simulation efficiency.

Contribution

A novel determinant quantum Monte Carlo approach that reduces the computational scaling from cubic to linear in inverse temperature for cluster solvers in dynamical mean-field theory.

Findings

Scales linearly with inverse temperature β

Sign problem remains comparable to Hirsch-Fye method

Enables more efficient low-temperature simulations

Abstract

Dynamical mean field theory and its cluster extensions provide a very useful approach for examining phase transitions in model Hamiltonians, and, in combination with electronic structure theory, constitute powerful methods to treat strongly correlated materials. The key advantage to the technique is that, unlike competing real space methods, the sign problem is well controlled in the Hirsch-Fye (HF) quantum Monte Carlo used as an exact cluster solver. However, an important computational bottleneck remains; the HF method scales as the cube of the inverse temperature, $\beta$. This often makes simulations at low temperatures extremely challenging. We present here a new method based on determinant quantum Monte Carlo which scales linearly in $\beta$, and demonstrate that the sign problem is identical to HF.