Gauge-invariant and anyonic-symmetric autoregressive neural network for quantum lattice models
Gauge-invariant and anyonic-symmetric autoregressive neural network for quantum lattice models
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DOI：
10.1103/physrevresearch.5.013216
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发表时间：
2021-01
影响因子：
4.2
通讯作者：
Di Luo;Zhuo Chen;Kaiwen Hu;Zhizhen Zhao;V. M. Hur;B. Clark
中科院分区：
文献类型：
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作者：
Di Luo;Zhuo Chen;Kaiwen Hu;Zhizhen Zhao;V. M. Hur;B. Clark
规范不变性和任意子对称性等对称性在量子多体物理学中起着至关重要的作用。我们开发了一种通用的方法来构建规范不变或任意对称自回归神经网络量子态，包括广泛的架构，如Transformer和递归神经网络（RNN），量子晶格模型。这些网络可以被有效地采样，并明确遵守规范对称性或任意子约束。我们证明，我们的方法可以提供精确的表示的基态和激发态的二维和三维复曲面代码，和X-cube分形子模型。我们变分优化我们的对称性纳入自回归神经网络的基态以及实时动态的各种模型。我们模拟了$U（1）格点规范理论量子链模型的动力学和基态，得到了二维SU（2）规范理论的相图，确定了SU（2）3任意链的相变和中心电荷，并计算了SU（2）不变海森堡自旋链的基态能量.我们的方法为探索凝聚态物理、高能物理和量子信息科学提供了强有力的工具。
Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum many-body physics. We develop a general approach to constructing gauge invariant or anyonic symmetric autoregressive neural network quantum states, including a wide range of architectures such as Transformer and recurrent neural network (RNN), for quantum lattice models. These networks can be efficiently sampled and explicitly obey gauge symmetries or anyonic constraint. We prove that our methods can provide exact representation for the ground and excited states of the 2D and 3D toric codes, and the X-cube fracton model. We variationally optimize our symmetry incorporated autoregressive neural networks for ground states as well as real-time dynamics for a variety of models. We simulate the dynamics and the ground states of the quantum link model of $\text{U(1)}$ lattice gauge theory, obtain the phase diagram for the 2D $\mathbb{Z}_2$ gauge theory, determine the phase transition and the central charge of the $\text{SU(2)}_3$ anyonic chain, and also compute the ground state energy of the SU(2) invariant Heisenberg spin chain. Our approach provides powerful tools for exploring condensed matter physics, high energy physics and quantum information science.