Abstract
We propose an extension of the quantum cluster algorithm by a combined use of the Fortuin-Kasteleyn mapping and the Hubbard-Stratonovich transformation. To describe the idea, we consider the $S=\frac{1}{2}$ $\mathrm{XXZ}$ chain model and express the partition function as the sum in an extended configuration space of spins, graphs, and fields. Then it is clarified that this algorithm possesses a computationally tractable continuous-time limit and maintains virtues of the quantum cluster algorithm. Numerical simulations are performed and its applicability is demonstrated. Further, we discuss potential gains in our algorithm.
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