Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter

TL;DR

This paper introduces an exactly solvable lattice Hamiltonian model for gapped boundaries in topological phases, classifies boundary excitations, and explores the algebraic structure of these boundaries.

Contribution

It provides a new solvable model for gapped boundaries in topological quantum systems and systematically analyzes their excitations and algebraic properties.

Findings

Classified boundary excitations in the model

Described bulk-to-boundary condensation process

Established algebraic/categorical framework for gapped boundaries

Abstract

We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also present the parallel algebraic/categorical structure of gapped boundaries.