arXiv subjects

Martin Bonkhoff

Publications and source records attributed to Martin Bonkhoff.

3 recordsLinked to original sources

arXiv2026

Symmetry and integrability in the anyon-Hubbard model

Recent cold atom experiments have realized one-dimensional anyons and enabled the tuning of 1D~statistics between bosons and fermions. Here, we analyze the symmetries, integrability, and resulting degeneracies of the underlying anyon-Hubbard model of finite length. Our results reveal a switching between symmetry classes AI, BDI, and CI in dependence on system size, particle number, and boundary conditions, and show that two anyons with periodic boundaries are integrable, while two anyons with open boundary conditions are not. We include a comprehensive analysis of all model limits, especially of interacting bosons and pseudofermions and resolve spectral signatures. We additionally reveal an exactly solvable doublon state that hides in the continuum of scattering states and the exact solution of the nullspace of two noninteracting anyons. The uncovered symmetries shape the fundamental properties of the one-dimensional anyons at hand, and the predicted states are accessible in state-of-the-art experiments.

cond-mat.quant-gas↗

arXiv2024

Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics

We study one-dimensional (1D) lattice anyons with extended Hubbard interactions at unit filling using bosonization and numerical simulations. The behavior can be continuously tuned from Bosonic to Fermionic behavior by adjusting the topological exchange angle $\theta$, which leads to a competition of different instabilities. We present the bosonization theory in presence of dynamic gauge fields, which predicts a phase diagrams of four different gapped phases with distinct dominant correlations. Advanced numerical simulations determine and analyze the exact phase transitions between Mott insulator, charge density wave, dimerized state, and Haldane insulator, all of which meet at a multi-critical line in the parameter space of anyonic angle $\theta$, onsite interaction $U$, and nearest neighbor repulsion $V$. Superfluid and pair-superfluid phases are stable in a region of small $V$.

cond-mat.str-el↗

arXiv2023

Coherence Properties of the Repulsive Anyon-Hubbard Dimer

One-dimensional anyonic models of the Hubbard type show intriguing ground-state properties, effectively transmuting between Bose-Einstein and Fermi-Dirac statistics. The simplest model that one can investigate is an anyonic version of the bosonic Josephson junction, the repulsive anyon-Hubbard dimer. In the following we find an exact duality relation to the Bethe-solvable Bose-Hubbard dimer, which is well known from quantum optics and information theory and has interesting connections to spin squeezing and entangled coherent states. Conversely, we show that the anyonic Hubbard dimer has nontrivial coherence properties that emerge from the anyonic statistics. In particular, we find that coherences can be suppressed and amplified and show that these features are remarkably robust against additional repulsive on-site interactions highlighting the distinct nature of anyons.

cond-mat.quant-gas↗