用限制玻尔兹曼机波函数重建玻色-哈伯德模型的Phase diagram
Phase diagram reconstruction of the Bose-Hubbard model with a Restricted Boltzmann Machine wavefunction
摘要：
最近，神经量子态用于描述多体和少体问题的基态已经越来越流行，因为它们的高表达性和处理难以处理的大希尔伯特空间的能力。特别是，基于变分蒙特卡罗的方法已被证明是成功的描述玻色子系统的物理，如玻色-哈伯德（BH）模型。然而，这种技术还没有系统地测试BH模型的参数空间，特别是在莫特绝缘体和超流相之间的边界。在这项工作中，我们评估的能力，变分Monte Carlo与一个试验波函数的限制玻尔兹曼机再现量子基态的BH模型的参数空间的几个点。为了基准的技术，我们比较其结果的基态通过精确对角化小一维链。在一般情况下，我们发现，学习的基态正确地估计许多可观的，复制到一个高度的第一莫特波瓣和第二个的一部分的相图。然而，我们发现，每当系统在激发流形之间转换时，该技术就受到挑战，因为在这些边界处没有正确地学习基态。我们通过提出一种丢弃在基态中学习到的噪声概率的方法来提高该技术产生的结果的质量。
英文摘要：
Recently, the use of neural quantum states for describing the ground state of many- and few-body problems has been gaining popularity because of their high expressivity and ability to handle intractably large Hilbert spaces. In particular, methods based on variational Monte Carlo have proven to be successful in describing the physics of bosonic systems such as the Bose-Hubbard (BH) model. However, this technique has not been systematically tested on the parameter space of the BH model, particularly at the boundary between the Mott insulator and superfluid phases. In this work, we evaluate the capabilities of variational Monte Carlo with a trial wavefunction given by a Restricted Boltzmann Machine to reproduce the quantum ground state of the BH model on several points of its parameter space. To benchmark the technique, we compare its results to the ground state found through exact diagonalization for small one-dimensional chains. In general, we find that the learned ground state correctly estimates many observables, reproducing to a high degree the phase diagram for the first Mott lobe and part of the second one. However, we find that the technique is challenged whenever the system transitions between excitation manifolds, as the ground state is not learned correctly at these boundaries. We improve the quality of the results produced by the technique by proposing a method to discard noisy probabilities learned in the ground state.
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