Abstract
Foliated fracton order is a qualitatively new kind of phase of matter. It is similar to topological order, but with the fundamental difference that a layered structure, referred to as a foliation, plays an essential role and determines the mobility restrictions of the topological excitations. In this work, we introduce a new kind of field theory to describe these phases: a foliated field theory. We also introduce a new lattice model and string-membrane-net condensation picture of these phases, which is analogous to the string-net condensation picture of topological order.
Highlights
Rather than giving a detailed description of this class of models in terms of abstract algebraic data, we demonstrate the construction through a simple example: the toric code, a lattice model for Z2 gauge theory
We have introduced a new foliated field theory and string-membrane-net model of foliated fracton order
The field theory and lattice model both seem to be capable of describing all currently-known abelian foliated fracton orders, such as the ones shown in Tab. 1
Summary
Fracton order [1, 2] is a recently theorized and remarkable type of phase of matter which is characterized by topological excitations with various kinds of mobility constraints. As a generalization of U(1) gauge theory, symmetric tensor gauge theories are naturally written as field theories, often with an E2+B2 kind of Hamiltonian The stabilility of these theories to spatial curvature was recently studied in Ref. Foliated (type-I) fracton models [1, 3, 32, 68, 69] can be characterized by their subdimensional particle excitations and a foliation structure [24], which is specified by stacks of layers in various directions. The field theory is inspired by a string-membrane-net model of foliated fracton order, which generalizes the X-cube model.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
