On the universal relations for the prefactors in correlation functions of 1D quantum liquids

TL;DR

This paper establishes universal relations between correlation function prefactors and formfactors in 1D quantum liquids, providing a theoretical foundation for understanding low-energy excitations and their contributions to asymptotic behaviors.

Contribution

It derives universal relations within the Luttinger model linking correlator prefactors to formfactors, enhancing the theoretical understanding of 1D quantum liquids.

Findings

Relations between correlator prefactors and formfactors are established.

Formulas for summing over particle-hole states are derived.

Predictions for low-lying particle-hole excitations are substantiated.

Abstract

For various one-dimensional quantum liquids in the framework of the Luttinger model (bosonization) we establish the relations between the coefficients before the power-law asymptotics of the correlators (prefactors) and the formfactors of the corresponding local operators. The derivation of these relations in the framework of the bosonization procedure allows to substantiate the prediction for the formfactors corresponding to the low-lying particle-hole excitations. We also obtain the formulas for the summation over the particle-hole states corresponding to the power-law asymptotics of the correlators.