Off-diagonal correlations of lattice impenetrable bosons in one dimension

D. M. Gangardt 1, G. V. Shlyapnikov 1, 2

New Journal of Physics 8 (2006) 167

We consider off-diagonal correlation functions of impenetrable bosons on a lattice. By using the Jordan-Wigner transformation the one-body density matrix is represented as (Toeplitz) determinant of a matrix of fermionic Green functions. Using the replica method we calculate exactly the full long-range asymptotic behaviour of the one-body density matrix. We discuss how subleading oscillating terms, originating from short-range correlations give rise to interesting features in the momentum distribution.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. Van der Waals-Zeeman Institute,
    University of Amsterdam