Exact Matrix Elements of the Field Operator in the Thermodynamic Limit of the Lieb-Liniger Model

Abstract

We study a matrix element of the field operator in the Lieb-Liniger model using the Bethe ansatz technique coupled with a functional approach to compute Slavnov determinants. We obtain the matrix element exactly in the thermodynamic limit for any coupling constant c, and compare our results to known semiclassics at the limit c → 0