Resummation-based quantum Monte Carlo for quantum paramagnetic phases

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 uncolored 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 an increase in (continuous) $N$, allowing the efficient simulation of quantum paramagnets. The underlying reason for the increased efficacy is the correspondence of quantum paramagnetic phases such as 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.