Berry Phases in the Bosonization of Nonlinear Edge Modes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916953670549504 |
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| author | Beauvillain, Mathieu Oblak, Blagoje Petropoulos, Marios |
| author_facet | Beauvillain, Mathieu Oblak, Blagoje Petropoulos, Marios |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_03991 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Berry Phases in the Bosonization of Nonlinear Edge Modes Beauvillain, Mathieu Oblak, Blagoje Petropoulos, Marios Mesoscale and Nanoscale Physics High Energy Physics - Theory Mathematical Physics Symplectic Geometry 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. |
| title | Berry Phases in the Bosonization of Nonlinear Edge Modes |
| topic | Mesoscale and Nanoscale Physics High Energy Physics - Theory Mathematical Physics Symplectic Geometry |
| url | https://arxiv.org/abs/2408.03991 |