论文标题
晶格上的手性阶段
Chiral Phases on the Lattice
论文作者
论文摘要
虽然手性量子场理论（QFTS）描述了从标准模型到拓扑量子物质的广泛物理系统，但由于Nielsen-Ninomiya定理以及可能存在量子异常，因此很难实现晶格上手性QFT。在本文中，我们使用物质手性阶段与手性量子场理论（QFTS）之间的联系来定义晶格上的手性QFT，并允许在数值上模拟一类巨大的外来场理论。我们的作品以“镜像费米恩”的方法为基础，该方法是在格子上定义手性理论的问题，该方法将手性场理论定义为手性阶段的边缘模式。我们首先回顾物质，手性领域理论和异常的深厚联系。然后，我们开发了$ SU（2）$手性领域理论的数值处理，并提供了半经典解决的Abelian $ 2+1 $手性拓扑订单的定义。这导致了零相关长度的手性$ u（1）$ spt阶段的完全可解决的定义，我们用来准确提取边缘手性场理论。这些零相关长度模型比以前的方法更简单，用于定义晶格上的手性场理论。
While chiral quantum field theories (QFTs) describe a wide range of physical systems, from the standard model to topological quantum matter, the realization of chiral QFTs on a lattice has proved to be difficult due to the Nielsen-Ninomiya theorem and the possible presence of quantum anomalies. In this thesis, we use the connection between chiral phases of matter and chiral quantum field theories (QFTs) to define chiral QFTs on a lattice and allow a huge class of exotic field theories to be simulated numerically. Our work builds on the 'mirror fermion' approach to the problem of defining chiral theories on a lattice, which defines chiral field theories as the edge modes of chiral phases. We begin by reviewing the deep connections between chiral phases of matter, chiral field theories, and anomalies. We then develop numerical treatments of an $SU(2)$ chiral field theory, and provide a semiclassically solvable definition of Abelian $2+1$ chiral topological orders. This leads to an exactly solvable definition of chiral $U(1)$ SPT phases with zero correlation length, which we use to extract the edge chiral field theories exactly. These zero-correlation length models are vastly more simple than previous approaches to defining chiral field theories on the lattice.
