Dynamical Spin Response of Doped Two-Leg Hubbard-like Ladders

TL;DR

This paper investigates the low-energy dynamical spin response of doped two-leg Hubbard-like ladders using an integrable SO(6) Gross-Neveu model, revealing incommensurate modes and scattering continua with exact form-factor calculations.

Contribution

It develops a method to compute form factors in the SO(6) Gross-Neveu model and applies it to analyze the spin susceptibility in doped ladders, including effects of perturbations.

Findings

Identifies incommensurate coherent spin modes near (π,π).

Characterizes broad scattering continua at other momentum points.

Provides exact low-energy susceptibility results using form-factor expansions.

Abstract

We study the dynamical spin response of doped two-leg Hubbard-like ladders in the framework of a low-energy effective field theory description given by the SO(6) Gross Neveu model. Using the integrability of the SO(6) Gross-Neveu model, we derive the low energy dynamical magnetic susceptibility. The susceptibility is characterized by an incommensurate coherent mode near $(\pi,\pi)$ and by broad two excitation scattering continua at other $k$-points. In our computation we are able to estimate the relative weights of these contributions. All calculations are performed using form-factor expansions which yield exact low energy results in the context of the SO(6) Gross-Neveu model. To employ this expansion, a number of hitherto undetermined form factors were computed. To do so, we developed a general approach for the computation of matrix elements of semi-local SO(6) Gross-Neveu operators. While our computation takes place in the context of SO(6) Gross-Neveu, we also consider the effects of perturbations away from an SO(6) symmetric model, showing that small perturbations at best quantitatively change the physics.