标题： 具有动力学费米子的格点规范场论的投影纠缠对态 显示英文标题

标题： Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions

摘要： 格点规范场论是研究标准模型和凝聚态物理中出现的规范场论的重要框架。然而，许多系统（或这些系统的某些区域）难以用传统的技术，例如基于作用的蒙特卡罗采样方法来研究。本文展示了如何使用规范化的高斯投影纠缠对态作为格点规范场论的变分波函数，该场论涉及动力学物理物质。我们研究了二维格点上的$\mathbb{Z}_2$规范理论，在每个格点上有单一味的费米子物质。我们的结果与通过精确对角化哈密顿量计算的结果一致，并且表明这种方法对于更大尺寸的系统在计算上是可行的，而这些系统无法获得精确解。这是朝着研究更高维度和其它规范群迈出的一步，同时在可控的计算成本下避免了符号问题。 显示英文摘要

摘要： Lattice gauge theory is an important framework for studying gauge theories that arise in the Standard Model and condensed matter physics. Yet many systems (or regimes of those systems) are difficult to study using conventional techniques, such as action-based Monte Carlo sampling. In this paper, we demonstrate the use of gauged Gaussian projected entangled pair states as an ansatz for a lattice gauge theory involving dynamical physical matter. We study a $\mathbb{Z}_2$ gauge theory on a two dimensional lattice with a single flavor of fermionic matter on each lattice site. Our results show agreement with results computed by exactly diagonalizing the Hamiltonian, and demonstrate that the approach is computationally feasible for larger system sizes where exact results are unavailable. This is a further step on the road to studying higher dimensions and other gauge groups with manageable computational costs while avoiding the sign problem.