Tomonaga-Luttinger Liquid Exponents of Correlation Functions around Fermi points in the Hubbard Model

TL;DR

This paper investigates the critical exponents of correlation functions in the one-dimensional Hubbard model under magnetic fields using conformal field theory, revealing how these exponents vary with magnetic field strength.

Contribution

It introduces a novel approach by solving dressed charge matrix equations with a fixed occupancy, providing new insights into magnetic field effects on correlation exponents.

Findings

Critical exponents increase monotonically with magnetic field.

Exponents approach definite values at zero magnetic field.

Method offers an alternative to traditional zero occupancy assumptions.

Abstract

The correlation functions of one-dimensional Hubbard model in the presence of external magnetic field was investigated through the conformal field technique. The long distance behaviour of the correlation functions and their critical exponents for the model in the presence of a magnetic field are established by solving the dressed charge matrix equations and setting the number of occupancies to one, as an alternative to the usual zero often used by authors in literatures. Our result shows the critical exponents of the correlation function grows monotonically with magnetic field and reduces to definite values at zero magnetic field around various Fermi points.