Self-Learning Determinantal Quantum Monte Carlo Method

TL;DR

This paper introduces a self-learning determinantal quantum Monte Carlo method that significantly accelerates simulations of interacting fermion systems, enabling large-scale and high-precision studies near critical points.

Contribution

It adapts the self-learning Monte Carlo approach to determinantal quantum Monte Carlo, achieving substantial speedups and enabling simulations on larger lattices with high accuracy.

Findings

Auto-correlation time reduced to near one near critical points

Achieved $ ext{O}(N)$-fold speedup in simulations

First simulation of a 100x100 lattice with high-precision critical exponents

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.