Parametric Ward-Takahashi identity in disordered systems and the integral identity associated with the Calogero-Sutherland model

TL;DR

This paper derives a parametric Ward-Takahashi identity for the Calogero-Sutherland model, revealing new symmetry relations in one-dimensional disordered systems with inverse square interactions, and explores their algebraic origins and potential generalizations.

Contribution

It introduces a novel parametric Ward-Takahashi identity specific to the Calogero-Sutherland model, connecting dynamical correlators and higher-order integrals of motion.

Findings

Identifies symmetry relations for specific coupling constants $, 1, 2$

Shows identities derive from the algebraic structure of the model

Conjectures generalization to arbitrary rational coupling 

Abstract

By utilizing the symmetric property known as the Ward-Takahashi identity in disordered systems, we explore the novel symmetry relations which hold in one-dimensional systems with inverse square interaction (the Calogero-Sutherland model). The identities emerge totally from the algebraic structure of the model. They show that the dynamical correlators are connected with one another, involving the higher-order integrals of motion. We obtain the result for the coupling strengths $\lambda=1/2, 1, and 2$, and conjecture that a similar relation may hold for arbitrary rational $\lambda$.