Dynamical Correlation Functions and Finite-size Scaling in Ruijsenaars-Schneider Model

TL;DR

This paper analyzes the dynamical correlation functions of the Ruijsenaars-Schneider model, revealing its low-energy behavior aligns with a $C=1$ Gaussian conformal field theory and introduces a new fractional quantum number selection rule.

Contribution

It provides the first evaluation of dynamical correlation functions and finite-size scaling in the Ruijsenaars-Schneider model, connecting it to conformal field theory with a novel quantum number rule.

Findings

Correlation functions evaluated in the thermodynamic limit.

Low-energy behavior matches $C=1$ Gaussian conformal field theory.

Identification of a new fractional quantum number selection rule.

Abstract

The trigonometric Ruijsenaars-Schneider model is diagonalized by means of the Macdonald symmetric functions. We evaluate the dynamical density-density correlation function and the one-particle retarded Green function as well as their thermodynamic limit. Based on these results and finite-size scaling analysis, we show that the low-energy behavior of the model is described by the $C=1$ Gaussian conformal field theory under a new fractional selection rule for the quantum numbers labeling the critical exponents.