Parts | Days | Selection | Search | Updates | Downloads | Help
Q: Fachverband Quantenoptik und Photonik
Q 43: Poster – Quantum Systems
Q 43.16: Poster
Wednesday, March 4, 2026, 17:00–19:00, Philo 2. OG
Bogoliubov theory of 1D anyons in a lattice — Bin-Han Tang1, •Axel Pelster2, and Martin Bonkhoff3 — 1University of Trento, Italy — 2RPTU Kaiserslautern-Landau, Germany — 3University of Hamburg, Germany
Anyons of the Hubbard type in 1D interpolate between bosonic and fermionic particle statistics. Their exclusion behavior is encoded in that of their parent particles, including statistical interactions dependent on the connectivity and form of the underlying Hamiltonian. Their exchange phase emerge via non-gaugable hopping processes that characteristically break spatio-temporal symmetries, away from their canonical limits. Both effects originate from density-dependent Peierls phases that are essentially non-perturbative. This results in a rich phenomenology but also in experimental challenges and the necessity of a careful theoretical treatment. To this end, we develop a generalized Bogoliubov theory for the bosonic version of the anyon-Hubbard model, maintaining periodicity in the statistical parameter and incorporating a condensation at finite momenta. We investigate the stability of the condensate and find a mean-field manifestation of the Pauli principle while transmuting from bosons to pseudo-fermions. We regularize characteristic divergences in the thermodynamic limit by the maximal momentum resolution of a finite periodic lattice. We determine the condensate depletion as well as its momentum self-consistently, and with this investigate excitations above ground-state as well as their universal parameters. We find a good agreement with Luttinger theory at weak coupling.
Keywords: anyon-Hubbard model; Bogoliubov theory; Luttinger theory; statistical interaction; sound velocities