Berry Phases in the Bosonization of Nonlinear Edge Modes

Abstract

We consider chiral, generally nonlinear density waves in one dimension, modelling the bosonized edge modes of a two-dimensional fermionic topological insulator. Using the coincidence between bosonization and Lie-Poisson dynamics on an affine U(1) group, we show that wave profiles which are periodic in time produce Berry phases accumulated by the underlying fermionic field. These phases can be evaluated in closed form for any Hamiltonian, and they serve as a diagnostic of nonlinearity. As an explicit example, we discuss the Korteweg-de Vries equation, viewed as a model of nonlinear quantum Hall edge modes.

20 pages, 6 figures. v2: Minor clarifications/footnotes added, two-column format, published in PRB

References in corpus (15)

• Quantum Computation as Geometry
• Fractional statistics in anyon collisions
• Realization of a fractional quantum Hall state with ultracold atoms
• Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
• Nonlinear Bosonization of Fermi Surfaces: The Method of Coadjoint Orbits
• Geometric actions for three-dimensional gravity
• Robustness of quantum Hall interferometry
• Linear and nonlinear edge dynamics of trapped fractional quantum Hall droplets
• Thomas Precession for Dressed Particles
• Anisotropic Quantum Hall Droplets
• Gate tunable edge magnetoplasmon resonators
• Effective field theory of Berry Fermi liquid from the coadjoint orbit method
• Quantum nonlinear optics on the edge of a few-particle fractional quantum Hall fluid in a small lattice
• Effective field theory for ersatz Fermi liquids
• Topological Bifurcations and Reconstruction of Travelling Waves