Resummation-based updates for Stochastic Series Expansion Quantum Monte Carlo

TL;DR

This paper introduces a resummation-based quantum Monte Carlo method that efficiently samples loop configurations for $SU(N)$ models, improving simulation performance for quantum paramagnets and linking quantum phases to classical loop-gas models.

Contribution

It develops a novel resummation technique for quantum Monte Carlo updates applicable to $SU(N)$ models, enhancing efficiency and establishing connections to classical loop-gas models.

Findings

Algorithmic performance improves with increasing N.

Efficient simulation of quantum paramagnets achieved.

Links between quantum phases and classical loop-gas models established.

Abstract

For spin rotational symmetric models with a positive-definite high-temperature expansion of the partition function, a stochastic sampling of the series expansion upon partial resummation becomes logically equivalent to sampling an uncoloured closely-packed loop-gas model in one higher dimension. Based on this, we devise quantum Monte Carlo updates that importance-sample loop configurations for general $SU(N)$ in fundamental and higher-symmetric representations. The algorithmic performance systematically improves with increase in (continuous) $N$ allowing efficient simulation of quantum paramagnets. The underlying reason for the increased efficacy is the correspondence of quantum paramagnetic phases like valence bond solids to short-loop phases on the loop-gas side rather than the particular value of $N$. This also gives a connection between Sandvik's $JQ$ model class and classical loop-gas models in the deconfined universality class.