An anyonic Hubbard model on a ladder at half-filling shows a metal-to-charge-density-wave transition and an effective strong-coupling model with four phases, including a Z2 phase and an incommensurate phase.
Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics
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abstract
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 $V$.
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Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling
An anyonic Hubbard model on a ladder at half-filling shows a metal-to-charge-density-wave transition and an effective strong-coupling model with four phases, including a Z2 phase and an incommensurate phase.