Off-diagonal correlations of lattice impenetrable bosons in one dimension

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 a (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.