Chiral Phases on the Lattice
Name
demarco-demarco-phd-physics-2022-thesis.pdf
Description
Thesis PDF
Size
5.31 MB
Format
Adobe PDF
Checksum (MD5)
ee659e39f4ee95c0b2f14edc49e9bf58
Author(s)
DeMarco, Michael Austin
Advisor(s)
Wen, Xiao-Gang
Date Issued
May 2022
Publisher
Massachusetts Institute of Technology
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
In Copyright - Educational Use Permitted
Copyright MIT
Persistent DSpace Link
