Erlangen 2022 – scientific programme
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A: Fachverband Atomphysik
A 25: Ultracold Atoms and Molecules I (joint session Q/A)
A 25.6: Talk
Thursday, March 17, 2022, 11:45–12:00, Q-H10
A lattice model for traid anyons — •Sebastian Nagies1, Botao Wang1, Nathan Harshman2, and André Eckardt1 — 1Institute of Theoretical Physics, Technical University Berlin, Berlin — 2Department of Physics, American University, Washington DC, USA
Hard-core two-body interactions in two dimensions leave the configuration space of particles not simply connected. This gives rise to anyons exhibiting fractional exchange statistics governed by the braid group. Recently it was pointed out that hardcore three-body interactions in one dimension leave similar defects in configuration space. This allows for novel exchange statistics described by the traid group, for which the Yang-Baxter relation no longer holds. Here we propose a lattice model realizing a specific abelian representation of this traid group. Our model uses bosons with number-dependent hopping phases to generate alternating bosonic and fermionic exchange phases. By combining numeric simulations with analytic derivation in the continuum limit, we find interesting ground state density distributions and energies that differ greatly from bosons, fermions and braid anyons. We define new traid anyon operators satisfying non-local commutation relations, and predict distinctive traid anyon quasi-momentum distributions. We discuss their possible relation with Haldane's exclusion statistics.