2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112135We 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.10 pages. Submitted to the Focus Issue on 'Cold Atoms in Optical Lattices' of New Journal of PhysicsStatistical Mechanicstext