Boundary States for Chiral Symmetries in Two Dimensions

TL;DR

This paper analyzes boundary states for 1+1 dimensional Dirac fermions with chiral symmetry, deriving formulas for boundary properties and classifying states based on topological phases related to Majorana modes.

Contribution

It provides explicit expressions for boundary central charge and ground state degeneracy, and classifies boundary states into two topological classes based on SPT phases.

Findings

Boundary states are classified into two topological classes.

Explicit formulas for boundary central charge and ground state degeneracy.

Connection between boundary states and Majorana zero modes.

Abstract

We study boundary states for Dirac fermions in d=1+1 dimensions that preserve Abelian chiral symmetries, meaning that the left- and right-moving fermions carry different charges. We derive simple expressions, in terms of the fermion charge assignments, for the boundary central charge and for the ground state degeneracy of the system when two different boundary conditions are imposed at either end of an interval. We show that all such boundary states fall into one of two classes, related to SPT phases supported by (-1)^F, which are characterised by the existence of an unpaired Majorana zero mode.