2008/02/14 by Raoul Santachiara, Pasquale Calabrese · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #cond-mat.mes-hall #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/1742-5468/2008/06/p06005
published as J. Stat. Mech. (2008) P06005 · 21 pages, 4 figures
arxiv created 2008/02/14 · openalex publication_date 2008/06/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
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 Painlevé 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.