Neural network representation for minimally entangled typical thermal states
Neural network representation for minimally entangled typical thermal states
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DOI：
10.1103/physrevb.106.165111
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发表时间：
2022-04
影响因子：
3.7
通讯作者：
D. Hendry;Hongwei Chen;A. Feiguin
中科院分区：
文献类型：
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作者：
D. Hendry;Hongwei Chen;A. Feiguin
最小纠缠典型热态（METTS）是一种可以求解量子多体系统虚时间演化的结构。通过使用弱纠缠的波函数，可以利用矩阵积态形式的有效表示。我们将这些思想推广到任意变分波函数中，作为例证，我们将重点放在受限玻尔兹曼机的特殊情况上。虚时间演化采用随机重构（自然梯度下降）方法，结合蒙特卡罗采样进行。由于时间演化发生在切空间上，因此希尔伯特空间中的实际路径与变分流形上的轨迹之间的偏差可能很重要，这取决于变分状态的内部结构和表达性。我们展示了这些差异如何转化为重新缩放的温度，并演示了该方法在一维和二维空间中的量子自旋系统中的应用。
Minimally entangled typical thermal states (METTS) are a construction that allows one to to solve for the imaginary time evolution of quantum many body systems. By using wave functions that are weakly entangled, one can take advantage of efficient representations in the form of matrix product states. We generalize these ideas to arbitrary variational wave functions and we focus, as illustration, on the particular case of restricted Boltzmann machines. The imaginary time evolution is carried out using stochastic reconfiguration (natural gradient descent), combined with Monte Carlo sampling. Since the time evolution takes place on the tangent space, deviations between the actual path in the Hilbert space and the trajectory on the variational manifold can be important, depending on the internal structure and expressivity of the variational states. We show how these differences translate into a rescaled temperature and demonstrate the application of the method to quantum spin systems in one and two spatial dimensions.