One-particle density matrix and momentum distribution function of one-dimensional anyon gases

Abstract

We present a systematic study of the Green functions of a one-dimensional gas of impenetrable anyons. We show that the one-particle density matrix is the determinant of a Toeplitz matrix whose large N asymptotic is given by the Fisher-Hartwig conjecture. We provide a careful numerical analysis of this determinant for general values of the anyonic parameter, showing in full details the crossover between bosons and fermions and the reorganization of the singularities of the momentum distribution function. We show that the one-particle density matrix satisfies a Painleve VI differential equation, that is then used to derive the small distance and large momentum expansions. We find that the first non-vanishing term in this expansion is always k^{-4}, that is proved to be true for all couplings in the Lieb-Liniger anyonic gas and that can be traced back to the presence of a delta function interaction in the Hamiltonian.

21 pages, 4 figures

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• Dynamical properties of hard-core anyons in one-dimensional optical lattices
• One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Strongly interacting mesoscopic systems of anyons in one dimension
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• Universal Tan relations for quantum gases in one dimension
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Higher-order local and non-local correlations for 1D strongly interacting Bose gas
• One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
• Zero temperature momentum distribution of an impurity in a polaron state of one-dimensional Fermi and Tonks-Girardeau gases
• One-body reduced density matrix of trapped impenetrable anyons in one dimension
• Off-diagonal correlations in one-dimensional anyonic models: A replica approach
• Quantum entanglement of particles on a ring with fractional statistics
• Correlation functions of one-dimensional strongly interacting two-component gases
• Ground state properties of hard-core anyons in a harmonic potential
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
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• Deviations from Off-Diagonal Long-Range Order in One-Dimensional Quantum Systems
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions
• Quantum Inverse Scattering Method with anyonic grading
• Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Fisher-Hartwig conjecture and the correlators in the inpenetrable Bose gas
• Large-Distance Asymptotic Behavior of the Correlation Functions of 1D Impenetrable Anyons at Finite Temperatures
• Non-conformal asymptotic behavior of the time-dependent field-field correlators of 1D anyons
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Quasimomentum distribution and expansion of an anyonic gas
• One-dimensional hard-core anyon gas in a harmonic trap 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
• Dualities for anyons
• Thermodynamics of Statistical Anyons
• Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Quench Dynamics of Anyon Tonks-Girardeau Gases