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.
Highlights
A fundamental principle of quantum statistical mechanics in three dimensions is the existence of two types of particles: bosons obeying Bose-Einstein statistics and fermions obeying Fermi-Dirac statistics
Since the reflection parity symmetry in the Hamiltonian is broken, we suggest below a modified Gutzwiller mean-field, which goes beyond the classical one found in literature [42,43,44,45] in order to include the influence of the fractional phase of anyons on the hopping dynamics
With the help of a fractional version of the Jordan-Wigner transformation, the Anyon-Hubbard model is mapped to the occupation-dependent hopping Bose-Hubbard model and, the Hilbert space of anyons can be constructed from that of bosons
Summary
A fundamental principle of quantum statistical mechanics in three dimensions is the existence of two types of particles: bosons obeying Bose-Einstein statistics and fermions obeying Fermi-Dirac statistics. Hao et al investigated how the fractional statistics affected the ground-state properties by mapping the hard-core anyonic Hamiltonian to a noninteracting fermionic system with a generalized Jordan-Wigner transformation [41]. In this paper we complement the previous studies of the ground-state properties of a 1D quantum gas of anyons confined in optical lattices To this end we map the Anyon-Hubbard model to an occupation-dependent hopping Bose-Hubbard model with the help of a fractional version of the Jordan-Wigner transformation. The ground-state properties of the 1D Anyon-Hubbard model are determined by studying the quasi-momentum distribution of anyons and bosons in both the hard-core and the soft-core case in Sec. 4 and Sec. 5 respectively.
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