论文标题
通过自动差异来缓解费米符号问题
Mitigating the fermion sign problem by automatic differentiation
论文作者
论文摘要
作为一种本质上无偏的方法，量子蒙特卡洛（QMC）方法对于模拟相互作用的量子系统至关重要。尽管QMC方法通常遭受臭名昭著的符号问题，但可以通过找到对模拟方案的更好选择来减轻量子模型的符号问题。但是，缺乏识别最佳QMC方案的一般框架。在这里，我们提出了一个使用自动差异化的通用框架，以自动搜索Hubbard-Stratonovich转换的给定ANSATZ中最佳的QMC方案，我们称之为“自动可区分符号优化”（ADSO）。我们将ADSO框架应用于Rashba Spin-Orbit耦合的Honeycomb晶格Hubbard模型，并证明ADSO在缓解甚至解决其符号问题方面非常有效。具体而言，ADSO在模型中找到了一个无标志点，以前被认为是标志性问题。对于ADSO发现的无标志模型，通过无标志QMC模拟显示其基态以具有螺旋磁有序。我们还获得了表征磁量子相变的临界指数。
As an intrinsically unbiased method, the quantum Monte Carlo (QMC) method is of unique importance in simulating interacting quantum systems. Although the QMC method often suffers from the notorious sign problem, the sign problem of quantum models may be mitigated by finding better choices of the simulation scheme. However, a general framework for identifying optimal QMC schemes has been lacking. Here, we propose a general framework using automatic differentiation to automatically search for the best QMC scheme within a given ansatz of the Hubbard-Stratonovich transformation, which we call "automatic differentiable sign optimization" (ADSO). We apply the ADSO framework to the honeycomb lattice Hubbard model with Rashba spin-orbit coupling and demonstrate that ADSO is remarkably effective in mitigating and even solving its sign problem. Specifically, ADSO finds a sign-free point in the model which was previously thought to be sign-problematic. For the sign-free model discovered by ADSO, its ground state is shown by sign-free QMC simulations to possess spiral magnetic ordering; we also obtained the critical exponents characterizing the magnetic quantum phase transition.
