Ground-state degeneracy for abelian anyons in the presence of gapped boundaries

TL;DR

This paper derives a comprehensive formula for calculating the ground-state degeneracy of abelian fractional quantum Hall phases with gapped boundaries, accounting for complex boundary conditions and domain walls.

Contribution

It introduces a general formula for ground-state degeneracy in abelian topological phases with intricate boundary configurations and domain walls.

Findings

Derived a universal formula for ground-state degeneracy

Applicable to complex boundary segmentations and domain walls

Enhances understanding of boundary effects in topological phases

Abstract

Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well-defined and can be computed using methods of Topological Quantum Field Theory. We derive a general formula for the ground-state degeneracy for abelian Fractional Quantum Hall phases, including the cases when connected components of the boundary are subdivided into an arbitrary number of segments, with a different boundary condition on each segment, and in the presence of an arbitrary number of boundary domain walls.