Fractonic Orders from Lattice Models and Field Theories

Citation

Ma, Xiuqi (2023) Fractonic Orders from Lattice Models and Field Theories. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/g80m-dy31. https://resolver.caltech.edu/CaltechTHESIS:06022023-010804337

Abstract

Fracton models are characterized by exotic features such as point-like excitations with restricted mobility, sub-extensive ground state degeneracy and UV/IR mixing. They have been studied previously using exactly solvable lattice models, higher rank gauge theories, etc. In an effort to classify fracton models into phases (i.e., fractonic orders), the so-called foliation structure has been introduced and shown to exist in many previously known models. A natural question then arises concerning the feasibility of the foliation paradigm in general. In this thesis, I study fracton models beyond the foliation paradigm and give simple diagnostics for the absence of a foliation structure. New notions of fractonic orders therefore need to be conceived, and I present such a conception which is a generalization of the foliation RG.

In Chapters 2 - 4, I introduce new fracton models obtained from infinite-component Chern-Simons (CS_∞) theories. By calculating observables such as ground state degeneracy and planon braiding statistics, I prove that most CS_∞ theories are not foliated. A CS_∞ theory can also be gapless with certain choices of parameters, and I show that such a theory is a stable gapless fracton model. Furthermore, I discuss topological features of a large subclass of gapless CS_∞ theories and present fully continuous effective field theories for this subclass.

In Chapters 5 - 6, I discuss a new notion of fractonic orders by studying the example of the Ising cage-net model. I begin by calculating the ground state degeneracy of the model, which shows that the model is not foliated. The calculation uses an operator algebra approach which relies only on intrinsic physical properties of the model rather than microscopic details, and I establish the framework of this approach conceptually and via examples. I then argue why this intrinsic approach, despite being a tool for calculation initially, may be a useful characterization of a fractonic order. Finally, I present a generalized foliation RG scheme, apply it to the Ising cage-net model, and discuss its limitations.

Thesis Files