Fractionally Quantized Berry Phase, Adiabatic Continuation, and Edge States

Abstract

Symmetry protected quantization of the Berry phase is discussed in relation to edge states. Assuming an existence of some adiabatic process which protects quantization of the Berry phase, non trivial Berry phase $\gamma =\pm 2\pi \rho$ ($\rho$ is a local filling of particles) for the bulk suggests appearance of edge states with boundaries. We have applied this generic consideration for Bloch states of some two dimensional model with massless Dirac fermions where $\gamma =\pm \pi /2$ implies the edge states. Entanglement entropy is evaluated for the models and its relation to the bulk-edge correspondence of Dirac fermions is discussed as well.

arXiv comment4 pages

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• Symmetry-protected quantization of complex Berry phases in non-Hermitian many-body systems
• Topological Order Parameters of the Spin-1/2 Dimerized Heisenberg Ladder in Magnetic Field
• Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
• Edge States of a Periodic Chain with Four-Band Energy Spectrum
• Topological surface states in dense solid hydrogen
• Hannay Angle: Yet Another Symmetry Protected Topological Order Parameter in Classical Mechanics
• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids
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