On the universal relations for the formfactors in 1D quantum liquids

TL;DR

This paper establishes universal relations between correlator prefactors and formfactors in 1D quantum liquids using bosonization, providing explicit formulas and supporting the prediction for low-lying excitations.

Contribution

It derives universal relations for formfactors and correlator prefactors in 1D quantum liquids within the Luttinger model framework, including explicit expressions and summation formulas.

Findings

Derived explicit formulas for particle-hole formfactors.

Established relations between correlator asymptotics and formfactors.

Supported predictions for low-lying particle-hole excitations.

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 present an explicit expressions for the particle-hole formfactors for various one-dimensional models. We also obtain the formulas for the summation over the particle-hole states corresponding to the power-law asymptotics of the correlators.