Berry phases in the bosonization of nonlinear edge modes
Phys. Rev. B 112, 125136 – Published 16 September, 2025
DOI: https://doi.org/10.1103/68f9-3td6
Abstract
We consider chiral, generally nonlinear density waves in one dimension, modeling 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.
