Off-diagonal correlations of lattice impenetrable bosons in one dimension

TL;DR

This paper derives the exact long-range asymptotic behavior of off-diagonal correlations in one-dimensional lattice impenetrable bosons, revealing how short-range effects influence momentum distribution features.

Contribution

It provides an exact calculation of the asymptotic form of the one-body density matrix for lattice impenetrable bosons using the replica method.

Findings

Exact asymptotic form of the one-body density matrix obtained

Identification of subleading oscillating terms affecting momentum distribution

Demonstration of the impact of short-range correlations on observable features

Abstract

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.