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A quantum Monte Carlo algorithm realizing an intrinsic relaxation

Tota Nakamura·Yoshiyuki Ito
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Abstract

We propose a new quantum Monte Carlo algorithm which realizes a relaxation intrinsic to the original quantum system. The Monte Carlo dynamics satisfies the dynamic scaling relation $τ\sim ξ^z$ and is independent of the Trotter number. Finiteness of the Trotter number just appears as the finite-size effect. An infinite Trotter number version of the algorithm is also formulated, which enables us to observe a true relaxation of the original system. The strategy of the algorithm is a compromise between the conventional worldline local flip and the modern cluster loop flip. It is a local flip in the real-space direction and is a cluster flip in the Trotter direction. The new algorithm is tested by the transverse-field Ising model in two dimensions. An accurate phase diagram is obtained.

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Tota Nakamura, Yoshiyuki Ito. 2003-05-14. A quantum Monte Carlo algorithm realizing an intrinsic relaxation. https://doi.org/10.1143/jpsj.72.2405

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