Bold Diagrammatic Monte Carlo technique for frustrated spin systems

TL;DR

This paper introduces a versatile diagrammatic Monte Carlo method for frustrated spin systems, enabling finite-temperature calculations across various dimensions and geometries, demonstrated through susceptibility computations on a triangular lattice.

Contribution

The authors develop a general fermionic diagrammatic Monte Carlo algorithm applicable to any dimension and lattice type for frustrated spin models, extending computational capabilities.

Findings

Computed uniform magnetic susceptibility matching high-temperature expansions.

Analyzed momentum-dependent static magnetic susceptibility across the Brillouin zone.

Validated the method's applicability to frustrated magnetic systems.

Abstract

Using fermionic representation of spin degrees of freedom within the Popov-Fedotov approach we develop an algorithm for Monte Carlo sampling of skeleton Feynman diagrams for Heisenberg type models. Our scheme works without modifications for any dimension of space, lattice geometry, and interaction range, i.e. it is suitable for dealing with frustrated magnetic systems at finite temperature. As a practical application we compute uniform magnetic susceptibility of the antiferromagnetic Heisenberg model on the triangular lattice and compare our results with the best available high-temperature expansions. We also report results for the momentum-dependence of the static magnetic susceptibility throughout the Brillouin zone.