The relevant excitations for the one-body function in the Lieb-Liniger model

TL;DR

This paper investigates the key excited states contributing to the one-body correlation function in the Lieb-Liniger model, identifying two-spinon-like excitations as significant through numerical and analytical methods.

Contribution

It proposes that two-spinon-like excitations dominate the small energy-momentum contributions in the Lieb-Liniger model and validates this with numerical and analytical evidence.

Findings

Two-spinon-like states are significant in the correlation function.

Numerical evaluation confirms the dominance of these excitations.

Analytical results support the conjecture in the strongly interacting regime.

Abstract

We study the ground state one-body correlation function in the Lieb-Liniger model. In the spectral representation, correlations are built from contributions stemming from different excited states of the model. We aim to understand which excited states carry significant contributions, specifically focusing on the small energy-momentum part of the dynamic one-body function. We conjecture that relevant excitations take form similar to two-spinon states known from XXZ spin chain. We validate this hypothesis by numerical evaluation of the correlator with ABACUS algorithm and by analytical computations in the strongly interacting regime.