Critical points of the anyon-Hubbard model

TL;DR

This paper investigates the phase transitions in the one-dimensional anyon-Hubbard model, revealing how the critical points and phase diagram depend on the statistical angle and density, using advanced numerical and quantum information methods.

Contribution

It determines the critical points and phase diagram of the anyon-Hubbard model, highlighting the effects of the statistical angle and density, and establishes universality with the Bose-Hubbard model at a specific angle.

Findings

Gapped and gapless phases are present regardless of the statistical angle.

Mott lobes vary with the statistical angle and density.

The model at $ heta = rac{ ight)$ shares universality with the Bose-Hubbard model.

Abstract

Anyons are particles with fractional statistics that exhibit a nontrivial change in the wavefunction under an exchange of particles. Anyons can be considered to be a general category of particles that interpolate between fermions and bosons. We determined the position of the critical points of the one-dimensional anyon-Hubbard model, which was mapped to a modified Bose-Hubbard model where the tunneling depends on the local density and the interchange angle. We studied the latter model by using the density matrix renormalization group method and observed that gapped (Mott insulator) and gapless (superfluid) phases characterized the phase diagram, regardless of the value of the statistical angle. The phase diagram for higher densities was calculated and showed that the Mott lobes increase (decrease) as a function of the statistical angle (global density). The position of the critical point separating the gapped and gapless phases was found using quantum information tools, namely the block von Neumann entropy. We also studied the evolution of the critical point with the global density and the statistical angle and showed that the anyon-Hubbard model with a statistical angle $\theta =\pi/4$ is in the same universality class as the Bose-Hubbard model with two body interactions.