Determinant representation for dynamical correlation functions of the Quantum nonlinear Schr\"odinger equation

TL;DR

This paper extends the determinant representation method for correlation functions to the quantum nonlinear Schrödinger equation, an interacting fermionic model, enabling the use of integrable differential equations for analysis.

Contribution

It demonstrates that determinant representations are applicable beyond free fermionic models, specifically for the quantum nonlinear Schrödinger equation.

Findings

Derived determinant representation for the correlation function of the model

Indicated potential for integrable equations and asymptotic analysis

Extended the applicability of determinant methods to interacting systems

Abstract

The foundation for the theory of correlation functions of exactly solvable models is determinant representation. Determinant representation permit to describe correlation functions by classical completely integrable differential equations [Barough, McCoy, Wu]. In this paper we show that determinant represents works not only for free fermionic models. We obtained determinant representation for the correlation function $<\psi(0,0)\psi^\dagger(x,t)>$ of the quantum nonlinear Schr\"odinger equation, out of free fermionic point. In the forthcoming publications we shall derive completely integrable equation and asymptotic for the quantum correlation function of this model of interacting fermions.