论文标题
纯$ \ mathbb {z} _3 $ gauge理论（2+1）d的变异蒙特卡洛仿真
Variational Monte Carlo simulation with tensor networks of a pure $\mathbb{Z}_3$ gauge theory in (2+1)d
论文作者
论文摘要
张量网络状态的变分最小化可以探索晶格规定的低能状态。但是，一般而言，高维张量网络状态的确切数值评估仍然具有挑战性。在[E. Zohar，J。I。Cirac，物理学。 Rev. D 97，034510（2018）]显示，通过将测量高斯投影的纠缠状状态与各种蒙特卡洛程序相结合，可以有效地计算物理可观察结果。在本文中，我们演示了如何使用这种方法来数字研究晶格仪理论的基态。更具体地说，我们基于此类收缩方法明确地执行了各种蒙特卡洛手术，用于在两个空间维度中使用$ \ mathbb {z} _3 $量表字段的纯尺度kogut-susskind hamiltonian进行。这是该方法的原理的第一个证明，它提供了增加变异参数数量的固有方法，并且可以很容易地扩展到具有物理费米子的系统。
Variational minimization of tensor network states enables the exploration of low energy states of lattice gauge theories. However, the exact numerical evaluation of high-dimensional tensor network states remains challenging in general. In [E. Zohar, J. I. Cirac, Phys. Rev. D 97, 034510 (2018)] it was shown how, by combining gauged Gaussian projected entangled pair states with a variational Monte Carlo procedure, it is possible to efficiently compute physical observables. In this paper we demonstrate how this approach can be used to investigate numerically the ground state of a lattice gauge theory. More concretely, we explicitly carry out the variational Monte Carlo procedure based on such contraction methods for a pure gauge Kogut-Susskind Hamiltonian with a $\mathbb{Z}_3$ gauge field in two spatial dimensions. This is a first proof of principle to the method, which provides an inherent way to increase the number of variational parameters and can be readily extended to systems with physical fermions.
