Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2008-02-14
J. Stat. Mech. (2008) P06005
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
21 pages, 4 figures
Scientific paper
10.1088/1742-5468/2008/06/P06005
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.
Calabrese Pasquale
Santachiara Raoul
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