论文标题

玻色 - 哈伯德模型的相图重建具有受限的玻尔兹曼机波函数

Phase diagram reconstruction of the Bose-Hubbard model with a Restricted Boltzmann Machine wavefunction

论文作者

Vargas-Calderón, Vladimir, Vinck-Posada, Herbert, González, Fabio A.

论文摘要

最近,由于其高度表达性和处理巨大的希尔伯特(Hilbert)空间的能力,使用神经量子状态描述了许多体型问题的基态。特别是,基于变异蒙特卡洛的方法已被证明在描述诸如Bose-Hubbard(BH)模型之类的骨系统物理学方面已成功。但是,该技术尚未在BH模型的参数空间上进行系统的测试,尤其是在Mott绝缘体和超氟相之间的边界上。在这项工作中,我们通过受限的玻尔兹曼机器(Boltzmann Machine)在其参数空间的几个点上对BH模型的量子接地状态进行了试验波函数评估。为了基准这项技术,我们将其结果与通过精确的一维链的对角线化发现的基态进行了比较。通常,我们发现学到的基态正确估计了许多可观察到的物品,并在高度重现了第一莫特·洛贝(Mott Lobe)的相图和第二个莫特(Mott Lobe)的一部分。但是,我们发现,每当激发歧管之间的系统过渡时,该技术就会受到挑战,因为在这些边界上无法正确学习基态。我们通过提出一种在基础状态中学到的嘈杂概率的方法来提高该技术产生的结果质量。

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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