The relationship between Hirsch-Fye and weak coupling diagrammatic Quantum Monte Carlo methods

TL;DR

This paper demonstrates the equivalence of two weak coupling CTQMC methods for Hubbard interactions, relates them to Hirsch-Fye QMC, and shows their convergence as the number of time slices increases, providing a diagrammatic interpretation.

Contribution

It establishes the equivalence between weak coupling CTQMC methods and Hirsch-Fye QMC, offering a new diagrammatic perspective and analyzing their behavior in the infinite time slices limit.

Findings

Weak coupling CTQMC methods are equivalent for Hubbard interactions.

Hirsch-Fye QMC is an approximation within CTQMC.

All methods converge as the number of time slices approaches infinity.

Abstract

Two weak coupling Continuous Time Quantum Monte Carlo (CTQMC) methods are shown to be equivalent for Hubbard-like interactions. A relation between these CTQMC methods and the Hirsch-Fye Quantum Monte Carlo (HFQMC) method is established, identifying the latter as an approximation within CTQMC and providing a diagrammatic interpretation. Both HFQMC and CTQMC are shown to be equivalent when the number of time slices in HFQMC becomes infinite, implying the same degree of fermion sign problem in this limit.