Continuous Time Quantum Monte Carlo method for fermions

TL;DR

This paper introduces a numerically exact continuous-time Quantum Monte Carlo algorithm for fermions with non-local interactions, enabling efficient simulations of complex multi-band, time-dependent systems without auxiliary field transformations.

Contribution

The paper presents a novel determinantal grand-canonical scheme based on stochastic series expansion, applicable to general non-local in space-time interactions for fermionic systems.

Findings

Successfully tested on exactly solvable models

Accurately computed Green functions and susceptibilities

Demonstrated applicability to multi-band super-symmetric models

Abstract

We present numerically exact continuous-time Quantum Monte Carlo algorithm for fermions with a general non-local in space-time interaction. The new determinantal grand-canonical scheme is based on a stochastic series expansion for the partition function in the interaction representation. The method is particularly applicable for multi-band time-dependent correlations since it does not invoke the Hubbard-Stratonovich transformation. The test calculations for exactly solvable models as well results for the Green function and for the time-dependent susceptibility of the multi-band super-symmetric model with a spin-flip interaction are discussed.