Form factors and correlation functions of an interacting spinless fermion model

TL;DR

This paper derives integral formulas for correlation functions of an interacting spinless fermion model using the fermionic R-operator, covering all interaction strengths and densities, and confirms known results in the free case.

Contribution

It introduces a fermionic R-operator and solves the inverse scattering problem for local fermion operators, providing new integral representations for correlation functions.

Findings

Derived multiple integral representations for correlation functions

Reproduced known results in the free fermion limit

Calculated form factors for finite systems

Abstract

Introducing the fermionic R-operator and solutions of the inverse scattering problem for local fermion operators, we derive a multiple integral representation for zero-temperature correlation functions of a one-dimensional interacting spinless fermion model. Correlation functions particularly considered are the one-particle Green's function and the density-density correlation function both for any interaction strength and for arbitrary particle densities. In particular for the free fermion model, our formulae reproduce the known exact results. Form factors of local fermion operators are also calculated for a finite system.