Ground-state properties of anyons in a one-dimensional lattice. (14th December 2015)

• Record Type: Journal Article
• Authors: Tang, Guixin; Eggert, Sebastian; Pelster, Axel
• Is Part Of: New journal of physics. Volume 17:Number 12(2015:Dec.)
• Publication Date: 2015-12-14
• Subjects: anyons -- Anyon–Hubbard model -- the fractional Jordan–Wigner transformation -- the quasi-momentum distribution -- one-dimensional lattice; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/17/12/123016
• Languages: English
• ISSNs: 1367-2630

Abstract

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.