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

TL;DR

This paper investigates how 1D lattice anyons with extended Hubbard interactions exhibit various phase transitions, revealing a rich phase diagram with multiple gapped phases and critical points influenced by fractional statistics.

Contribution

It introduces a combined bosonization and numerical approach to analyze phase transitions in 1D anyonic systems with extended interactions, highlighting the tunability of phases via the exchange angle.

Findings

Identification of four distinct gapped phases with unique correlations.

Existence of a multi-critical line where multiple phases meet.

Stability of superfluid phases at low nearest neighbor repulsion.

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 $V$.