Ground state properties of hard-core anyons in a harmonic potential

Abstract

Using anyon-fermion mapping method, we investigate the ground state properties of hard-core anyons confined in a one-dimensional harmonic trap. The concise analytical formula of the reduced one-body density matrix are obtained. Basing on the formula, we evaluated the momentum distribution, the natural orbitals and their occupation distributions for different statistical parameters. The occupation and occupation fraction of the lowest natural orbital versus anyon number are also displayed. It is shown that the ground state properties of anyons interplay between Bosons and Fermions continuously. We can expect that the hard-core anyons of larger statistical parameter exhibit the similar properties to the hard-core Bosons although anyon system satisfy specific fractional statistics.

6 pages, 7 figures

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• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Correlation functions of one-dimensional strongly interacting two-component gases
• Deviations from Off-Diagonal Long-Range Order in One-Dimensional Quantum Systems
• Universal off-diagonal long-range order behaviour for a trapped Tonks-Girardeau gas
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions
• One-dimensional hard-core anyon gas in a harmonic trap at finite temperature
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Natural orbitals and their occupation numbers for free anyons in the magnetic gauge
• One-dimensional anyons in relativistic field theory
• Quench Dynamics of Anyon Tonks-Girardeau Gases