Resummation-based updates for Stochastic Series Expansion Quantum Monte Carlo

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.

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Cited by in corpus (8)

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• Quantum optimization within lattice gauge theory model on a quantum simulator
• Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
• Magnetic effects of non-magnetic impurities in gapped short-range resonating valence bond spin liquids
• Pseudocriticality in antiferromagnetic spin chains
• Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(\pi ,\pi )$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets
• Accessing Excitation of Many-body Systems via Single-Mode Approximation within Quantum Monte Carlo Simulations
• Notes on resummation-based quantum Monte Carlo vis-à-vis sign-problematic Heisenberg models on canonical geometrically frustrated lattices