You are cordially invited to the SCL seminar of the Center for the Study of Complex Systems, which will be held on Monday, 28 September 2026 at 14:00 in the "Zvonko Marić" lecture hall of the Institute of Physics Belgrade. The talk entitled

Bogoliubov theory of 1D anyons in a lattice

will be given by Axel Pelster (Physics Department and Research Center OPTIMAS, RPTU Kaiserslautern-Landau, Germany). The abstract of the talk:

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 [1,2] and the necessity of a careful theoretical treatment [3,4].

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.


References:

[1] J. Kwan, et al., Realization of one-dimensional anyons with arbitrary
statistical phase, Science 386, 1055 (2024).
[2] S. Dhar, et al., Observing anyonization of bosons in a quantum gas, Nature 642, 53 (2025).
[3] M. Bonkhoff, et al., Bosonic continuum theory of one-dimensional lattice anyons, Phys. Rev. Lett. 126, 163201 (2021).
[4] M. Bonkhoff, et al., Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics, Phys. Rev. Lett. 135, 036601 (2025).