# Three-body interaction effects on the ground state of one-dimensional anyons

## TL;DR

This paper investigates how three-body interactions and anyonic statistics influence the ground state and phase transitions in a one-dimensional anyon-Hubbard model, revealing novel superfluid regions and phase behavior.

## Contribution

It introduces a modified Bose-Hubbard model incorporating three-body interactions and analyzes the effects of anyonic statistics on quantum phases and transitions.

## Key findings

- Quantum phase transition driven by statistics observed.
- Absence of Mott insulator with one particle per site depends on anyonic angle.
- Three distinct superfluid regions identified for larger anyonic angles.

## Abstract

A quantum phase transition driven by the statistics was observed in an anyon-Hubbard model with local three-body interactions. Using a fractional Jordan-Wigner transformation, we arrived at a modified Bose-Hubbard model, which exhibits Mott insulator and superfluid phases. The absence of a Mott insulator state with one particle per site depends on the anyonic angle, and a quantum phase transition from a superfluid to a Mott insulator state is obtained for a fixed value of the hopping. The critical points were estimated with the von Neumann block entropy and increase as the hopping grows. The statistics modify the ground state, and three different superfluid regions were observed for larger values of the anyonic angle.