Ground-state properties of anyons in a one-dimensional lattice

TL;DR

This paper investigates the ground-state properties of anyons in a one-dimensional lattice using a combination of analytical and numerical methods, revealing unique momentum distribution features due to their fractional statistics.

Contribution

It introduces a mapping of anyon dynamics to a Bose-Hubbard model and applies a modified Gutzwiller approach alongside DMRG to analyze their ground-state properties.

Findings

Anyonic quasi-momentum distribution shows peak-shift and asymmetry.

Asymmetry in the bosonic distribution depends on particle density.

The fractional phase influences the many-body wavefunction significantly.

Abstract

Using the Anyon-Hubbard Hamiltonian, we analyze the ground-state properties of anyons in a one-dimensional lattice. To this end we map the hopping dynamics of correlated anyons to an occupation-dependent hopping Bose-Hubbard model using the fractional Jordan-Wigner transformation. In particular, we calculate the quasi-momentum distribution of anyons, which interpolates between Bose-Einstein and Fermi-Dirac statistics. Analytically, we apply a modified Gutzwiller mean-field approach, which goes beyond a classical one by including the influence of the fractional phase of anyons within the many-body wavefunction. Numerically, we use the density-matrix renormalization group by relying on the ansatz of matrix product states. As a result it turns out that the anyonic quasi-momentum distribution reveals both a peak-shift and an asymmetry which mainly originates from the nonlocal string property. In addition, we determine the corresponding quasi-momentum distribution of the Jordan-Wigner transformed bosons, where, in contrast to the hard-core case, we also observe an asymmetry for the soft-core case, which strongly depends on the particle number density.