  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.
