Entanglement Hamiltonians for chiral fermions with zero modes

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.

typos fixed

References in corpus (8)

• Towards a derivation of holographic entanglement entropy
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Electron fractionalization in two-dimensional graphenelike structures
• Entanglement hamiltonians in two-dimensional conformal field theory
• A note on the Full Counting Statistics of paired fermions
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Long range order and symmetry breaking in Projected Entangled Pair State models
• Entanglement Hamiltonian of the quantum Néel state

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