Charge and spin response functions for the Tomonaga model with quadratic dispersion and different interactions

TL;DR

This paper derives analytical and numerical expressions for charge and spin response functions in the Tomonaga model with quadratic dispersion, considering various interactions and ground state correlations.

Contribution

It provides new analytical formulas and a matrix diagonalization approach for response functions with different interactions in the quadratic dispersion Tomonaga model.

Findings

Analytic expressions for constant interaction case

Matrix diagonalization method for general interactions

Discussion of power-law behavior in dynamic structure factors

Abstract

We derive expressions for the charge and spin response function for the Tomonaga model with quadratic dispersion and arbitrary (but finite for zero momentum) interaction. For constant interaction these expressions are analytic and for other types of interaction only a simple matrix has to be diagonalised. We use a truncated expansion in particle-hole states with and without inclusion of correlations in the ground state yielding an exact result for pure intra-band interaction. We also discuss the possibility of power-laws in the dynamic structure factor for the spinful and spinless model.