Strong-coupling diagrammatic Monte Carlo technique for correlated fermions and frustrated spins

TL;DR

This paper introduces a new strong-coupling diagrammatic Monte Carlo method applicable to fermionic and spin systems, using a recursive, non-perturbative approach based on Wick's theorem, enabling unbiased and systematic calculations.

Contribution

The authors develop a novel strong-coupling Monte Carlo technique that avoids Grassmannian transformations, allowing for exact, non-perturbative treatment of local physics in correlated fermions and spins.

Findings

Excellent agreement with numerical linked cluster expansion

Method is controllable and unbiased

Applicable to a wide range of fermionic and spin models

Abstract

We describe a controllable and unbiased strong-coupling diagrammatic Monte Carlo technique that is applicable to a wide range of fermionic systems and spin models. Unlike previous strong coupling methods that generally rely on the Grassmannian Hubbard-Stratonovich transformation, our construction is based on Wick's theorem and a recursive procedure to group contractions into effective connected vertices that are non-perturbative in all local physics and can be calculated exactly. The resulting expansion is described by simple diagrammatic rules that make it suitable for systematic treatment via stochastic sampling. Benchmarks against numerical linked cluster expansion display excellent agreement.