论文标题
使用费米金张量网络找到晶格量规理论的基态：$ 2+1d $ $ \ $ \ mathbb {z} _2 $示范
Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ $\mathbb{Z}_2$ demonstration
论文作者
论文摘要
张量的网络状态，特别是预计的纠缠对状态（PEPS），这是对复杂量子多体系统的变异研究的强大ANSATZ，这要归功于它们的内置纠缠熵区法律。在这项工作中，我们使用一种特殊的Peps -Guauged Gaussian Fermionic Peps（GGFPEPS）来找到$ 2+1D $ dimensional pure $ \ Mathbb {Z} _2 $ lattice Gauge的基础状态，以了解广泛的构造代数。我们通过将PEPS方法与蒙特卡洛计算相结合，从而有效地收缩了PEPS和相关函数的计算。以前，这种数值计算涉及计算具有系统尺寸的基质缩放的Pfaffian，从而形成严重的瓶颈。在这项工作中，我们展示了如何克服这个问题。这为我们在此处提出的方法和基准测试的方法铺平了道路，以有效的，无标志的方式使用费米金物质的较高维度和模型。
Tensor network states, and in particular Projected Entangled Pair States (PEPS) have been a strong ansatz for the variational study of complicated quantum many-body systems, thanks to their built-in entanglement entropy area law. In this work, we use a special kind of PEPS - Gauged Gaussian Fermionic PEPS (GGFPEPS) to find the ground state of $2+1d$ dimensional pure $\mathbb{Z}_2$ lattice gauge theories for a wide range of coupling constants. We do so by combining PEPS methods with Monte-Carlo computations, allowing for efficient contraction of the PEPS and computation of correlation functions. Previously, such numerical computations involved the calculation of the Pfaffian of a matrix scaling with the system size, forming a severe bottleneck; in this work we show how to overcome this problem. This paves the way for applying the method we propose and benchmark here to other gauge groups, higher dimensions, and models with fermionic matter, in an efficient, sign-problem-free way.
