Entanglement Hamiltonians for chiral fermions with zero modes

TL;DR

This paper investigates how topological zero modes influence the entanglement Hamiltonians and entropy in (1+1)d free chiral fermion systems, providing explicit formulas and analyzing boundary condition effects.

Contribution

It introduces a method combining Riemann-Hilbert solutions and finite rank perturbation theory to explicitly compute entanglement Hamiltonians with zero modes.

Findings

Explicit expression for entanglement Hamiltonian with zero modes.

Exact formula for entropy change due to zero modes.

Analysis of boundary condition effects on entanglement.

Abstract

In this Letter we study the effect of topological zero modes on entanglement Hamiltonians and entropy of free chiral fermion systems in (1+1)d. We show how Riemann-Hilbert solutions combined with finite rank perturbation theory allow us to obtain explicit expressions for entanglement Hamiltonians. We consider both chiral Majorana and Dirac fermions, and explore the effects of boundary conditions (periodic/anti-periodic for Majorana and generic for Dirac) and associated zero modes on entanglement. In the periodic sector, we derive explicitly the non-local contribution to the entanglement Hamiltonian due to the zero mode, and show an exact expression for the change in entanglement entropy due to the zero mode.