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arXiv · 1612.03804

Self-Learning Determinantal Quantum Monte Carlo Method

Xiao Yan Xu·Yang Qi·Junwei Liu·Liang Fu·Zi Yang Meng
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Abstract

Self-learning Monte Carlo method [arXiv:1610.03137, 1611.09364] is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we implement this method in the framework of determinantal quantum Monte Carlo simulation of interacting fermion systems. Guided by a self-learned bosonic effective action, our method uses a cumulative update [arXiv:1611.09364] algorithm to sample auxiliary field configurations quickly and efficiently. We demonstrate that self-learning determinantal Monte Carlo method can reduce the auto-correlation time to as short as one near a critical point, leading to $\mathcal{O}(N)$-fold speedup. This enables to simulate interacting fermion system on a $100\times 100$ lattice for the first time, and obtain critical exponents with high accuracy.

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Xiao Yan Xu, Yang Qi, Junwei Liu, Liang Fu, Zi Yang Meng. 2016-12-12. Self-Learning Determinantal Quantum Monte Carlo Method. https://doi.org/10.1103/physrevb.96.041119

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