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

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.

arXiv comment11 pages, 5 figures

References in corpus (32)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• The density-matrix renormalization group in the age of matrix product states
• Cold bosonic atoms in optical lattices
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• Strongly Correlated Quantum Walks in Optical Lattices
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Second Renormalization of Tensor-Network States
• Statistically induced Phase Transitions and Anyons in 1D Optical Lattices
• Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains
• Exact solution of double-delta function Bose gas through interacting anyon gas
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Photon-Assisted Tunneling in a Biased Strongly Correlated Bose Gas
• Phase diagram of the extended Bose Hubbard model
• The Anyon Hubbard Model in One-Dimensional Optical Lattices
• Probabilities and Path-Integral Realization of Exclusion Statistics
• Simulating quantum statistics with entangled photons: a continuous transition from bosons to fermions
• Correlation functions of one-dimensional anyonic fluids
• Nonequilibrium dynamics of one-dimensional hard-core anyons following a quench: Complete relaxation of one-body observables
• Accurate determination of the Gaussian transition in spin-1 chains with single-ion anisotropy
• Ground-state properties of one-dimensional anyon gases
• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• Generalized exclusion statistics and degenerate signature of strongly interacting anyons
• Bethe Ansatz for 1D interacting anyons
• Dynamical properties of hard-core anyons in one-dimensional optical lattices
• Quantum Walks of Two Interacting Anyons in 1D Optical Lattices
• Perturbative corrections to the Gutzwiller mean-field solution of the Mott-Hubbard model
• Berry phase induced dimerization in one-dimensional quadrupolar systems
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model

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• Anyonic tight-binding models of parafermions and of fractionalized fermions
• Critical points of the anyon-Hubbard model
• Ground State Properties of the One-Dimensional Unconstrained Pseudo-Anyon Hubbard Model
• Anyonic Haldane insulator in one dimension
• Non-equilibrium Floquet steady states of time-periodic driven Luttinger liquids
• Probing the exchange statistics of one-dimensional anyon models
• Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the Lieb-Liniger model
• Strongly repulsive anyons in one dimension
• Creating anyons from photons using a nonlinear resonator lattice subject to dynamic modulation
• Three-body interaction effects on the ground state of one-dimensional anyons
• Statistically related many-body localization in the one-dimensional anyon Hubbard model
• Floquet-Induced Superfluidity with Periodically Modulated Interactions of Two-Species Hardcore Bosons in a One-dimensional Optical Lattice
• Statistically induced topological phase transitions in a one-dimensional superlattice anyon-Hubbard model
• Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
• Modeling free anyons at the bosonic and fermionic ends
• Anyon optics with time-of-flight two-particle interference of double-well-trapped interacting ultracold atoms
• Quantum computation from fermionic anyons on a 1D lattice
• Numerical simulation of non-abelian anyons
• Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics
• Quasimomentum distribution and expansion of an anyonic gas
• Quantum walk of two anyons across a statistical boundary
• Driven Bose-Hubbard Model with a Parametrically Modulated Harmonic Trap
• Coherence Properties of the Repulsive Anyon-Hubbard Dimer
• Two-site anyonic Josephson junction
• Thermodynamics of Statistical Anyons
• Beats, broken-symmetry superfluid on a one dimensional anyon Hubbard model
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Encoding a topological gauge theory on a ring-shaped Raman-coupled Bose gas
• Boson-Anyon-Fermion Mapping and Anyon Construction in One Dimension
• One-dimensional anyons in relativistic field theory