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

Understand

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.