Notes on resummation-based quantum Monte Carlo vis-\`a-vis sign-problematic Heisenberg models on canonical geometrically frustrated lattices

TL;DR

This paper investigates the effectiveness of resummation-based quantum Monte Carlo methods on frustrated Heisenberg models, finding that it does not alleviate the sign problem on certain geometrically frustrated lattices.

Contribution

It demonstrates that resummation-based QMC does not reduce the sign problem for frustrated SU(2)-symmetric Heisenberg antiferromagnets on triangular lattices.

Findings

Resummation-based updates improve ergodic sampling.

Sign problem remains severe on frustrated lattices.

Potential insights for designing better algorithms.

Abstract

We show here that a direct application of resummation-based quantum Monte Carlo (QMC) -- implemented recently for sign-problem-free SU(2)-symmetric Hamiltonians in the stochastic series expansion (SSE) framework -- does not reduce the sign problem for frustrated SU(2)-symmetric Heisenberg antiferromagnets on canonical geometrically frustrated lattices composed of triangular motifs such as the triangular lattice. In the process, we demonstrate that resummation-based updates do provide an ergodic sampling of the SSE-based QMC configurations which can be an issue when using the standard SSE updates, however, severely limited by the sign problem as previously mentioned. The notions laid out in these notes may be useful in the design of better algorithms for geometrically frustrated magnets.