Dynamically enriched topological orders in driven two-dimensional systems

TL;DR

This paper explores new dynamical topological phases in 2D quantum systems driven periodically, introducing models for Floquet symmetry protected topological phases and enriched topological orders, revealing novel boundary states and anyon transmutations.

Contribution

It constructs solvable lattice models for 2D bosonic FSPT phases and FET orders, expanding the understanding of dynamical topological phenomena beyond equilibrium.

Findings

Bosonic FSPTs act as topological pumps depositing 1D SPT loops on boundaries.

Coupling FSPTs to gauge fields yields models with transmuting anyon excitations.

Examples of 'beyond cohomology' FET orders demonstrate topological pumping of emergent anyons.

Abstract

Time-periodic driving of a quantum system can enable new dynamical topological phases of matter that could not exist in thermal equilibrium. We investigate two related classes of dynamical topological phenomena in 2D systems: Floquet symmetry protected topological phases (FSPTs), and Floquet enriched topological orders (FETs). By constructing solvable lattice models for a complete set of 2D bosonic FSPT phases, we show that bosonic FSPTs can be understood as topological pumps which deposit loops of 1D SPT chains onto the boundary during each driving cycle, which protects a non-trivial edge state by dynamically tuning the edge to a self-dual point poised between the 1D SPT and trivial phases of the edge. By coupling these FSPT models to dynamical gauge fields, we construct solvable models of FET orders in which anyon excitations are dynamically transmuted into topologically distinct anyon types during each driving period. These bosonic FSPT and gauged FSPT models are classified by group cohomology methods. In addition, we also construct examples of "beyond cohomology" FET orders, which can be viewed as topological pumps of 1D topological chains formed of emergent anyonic quasi-particles.