Mainz 2026 – scientific programme

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SYMB: Symposium One-Dimensional Quantum Many-Body Systems between Bose and Fermi Statistics

SYMB 1: One-Dimensional Quantum Many-Body Systems between Bose and Fermi Statistics

SYMB 1.2: Invited Talk

Thursday, March 5, 2026, 15:00–15:30, P 1

Non trivial particle exchange in one dimension: The anyon Hubbard model and beyond — •André Eckardt — Institut für Physik und Astronomie, TU Berlin, Berlin

The anyon Hubbard model has recently been investigated experimentally both by the Greiner group in Harvard in a driven optical lattice and by the Nägerl group in Innsbruck by means of impurities. It can be represented by a bosonic tight-binding chain with number-dependent Peierls phases. I will given an introduction to the model and argue that it describes non-trivial particle exchange in one spatial dimension, associated with non-trivial Berry phases around Fock-space loops. Also its bound states in and out of the continuum will be addressed. Finally, I will discuss a recently proposed lattice model for so-called traid anyons, which are associated with the non-trivial braiding of three particles in their two-dimensional relative space.