Continuous Time Quantum Monte Carlo Method for Fermions: Beyond Auxiliary Field Framework

TL;DR

This paper introduces a numerically exact continuous-time Quantum Monte Carlo algorithm for fermionic systems with non-local interactions, avoiding the Hubbard-Stratonovich transformation and enabling advanced multi-band, time-dependent correlation studies.

Contribution

It presents a novel determinantal grand-canonical method based on stochastic series expansion, extending quantum Monte Carlo techniques beyond traditional auxiliary field frameworks.

Findings

Accurate Green function calculations for multi-orbital models

Successful simulation of time-dependent susceptibility in complex impurity systems

Demonstrates applicability to non-local and multi-band interactions

Abstract

Numerically exact continuous-time Quantum Monte Carlo algorithm for finite fermionic systems with non-local interactions is proposed. The scheme is particularly applicable for general multi-band time-dependent correlations since it does not invoke Hubbard-Stratonovich transformation. The present determinantal grand-canonical method is based on a stochastic series expansion for the partition function in the interaction representation. The results for the Green function and for the time-dependent susceptibility of multi-orbital super-symmetric impurity model with a spin-flip interaction are presented.