Quasi continuous-time impurity solver for the dynamical mean-field theory with linear scaling in the inverse temperature

TL;DR

This paper introduces a highly precise and efficient impurity solver for dynamical mean-field theory that scales linearly with inverse temperature, enabling accurate low-temperature simulations.

Contribution

The authors develop a numerically exact impurity solver combining BSS-QMC with multigrid extrapolation, achieving linear scaling in inverse temperature for DMFT calculations.

Findings

Results are free of significant Trotter errors.

Method shows linear scaling with inverse temperature.

Accurate near the Mott transition in the Hubbard model.

Abstract

We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary Hamiltonian, for which the Green function is computed by combining determinantal quantum Monte Carlo (BSS-QMC) calculations with a multigrid extrapolation procedure. The method is numerically exact, i.e., yields results which are free of significant Trotter errors, but retains the BSS advantage, compared to direct QMC impurity solvers, of linear (instead of cubic) scaling with the inverse temperature. The new algorithm is applied to the half-filled Hubbard model close to the Mott transition; detailed comparisons with exact diagonalization, Hirsch-Fye QMC, and continuous-time QMC are provided.