Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins

TL;DR

This paper introduces a diagrammatic Monte Carlo method for strongly correlated lattice spins, demonstrating its effectiveness on the triangular lattice Heisenberg model and revealing insights into its magnetic properties.

Contribution

It applies a fermionization-based diagrammatic Monte Carlo approach to frustrated spins, showing convergence and providing new microscopic insights into the model's magnetic behavior.

Findings

Finite convergence radius due to sign blessing

Accurate correspondence with classical model at finite temperatures

Indications of no magnetic order at zero temperature

Abstract

We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo sampling of skeleton Feynman diagrams within the fermionization framework offers a universal first-principles tool for strongly correlated lattice quantum systems. We observe the fermionic sign blessing---cancellation of higher order diagrams leading to a finite convergence radius of the series. We calculate the magnetic susceptibility of the triangular-lattice quantum antiferromagnet in the correlated paramagnet regime and reveal a surprisingly accurate microscopic correspondence with its classical counterpart at all accessible temperatures. The extrapolation of the observed relation to zero temperature suggests the absence of the magnetic order in the ground state. We critically examine the implications of this unusual scenario.