Floquet codes and phases in twist-defect networks

TL;DR

This paper introduces paired twist-defect networks that unify Floquet codes, adiabatic Hamiltonian loops, and Floquet topological orders, enabling topological analysis of code dynamics and revealing topological obstructions in specific models.

Contribution

It establishes a formalism connecting Floquet codes with topological phases and provides new models with customizable anyon-automorphism dynamics.

Findings

Honeycomb Floquet code has an irrational chiral Floquet index

Topological obstructions prevent simple boundary formation in certain codes

Generalized codes exhibit arbitrary anyon-automorphism dynamics

Abstract

We introduce a class of models, dubbed paired twist-defect networks, that generalize the structure of Kitaev's honeycomb model for which there is a direct equivalence between: i) Floquet codes (FCs), ii) adiabatic loops of gapped Hamiltonians, and iii) unitary loops or Floquet-enriched topological orders (FETs) many-body localized phases. This formalism allows one to apply well-characterized topological index theorems for FETs to understand the dynamics of FCs, and to rapidly assess the code properties of many FC models. As an application, we show that the Honeycomb Floquet code of Haah and Hastings is governed by an irrational value of the chiral Floquet index, which implies a topological obstruction to forming a simple, logical boundary with the same periodicity as the bulk measurement schedule. In addition, we construct generalizations of the Honeycomb Floquet code exhibiting arbitrary anyon-automorphism dynamics for general types of Abelian topological order.