Tomonaga-Luttinger Unusual Exponents around Fermi Points in the One-Dimensional Hubbard Model

Abstract

We study the correlation functions of one-dimensional Hubbard model in the presence of external magnetic field through the conformal field method. The long distance behaviour of the correlation functions and their unusual exponents for the model in the presence of a magnetic field are developed by solving the dressed charge matrix equations and setting the number of occupancies to one, as alternative to the usual zero used by authors in literatures. This work shows that the exponent of the correlation functions is a monotonous function of magnetic field and the correlation functions decay as powers of these unusual exponents. As the magnetic field goes to zero, we obtain the exponents as 8.125, 11.125, 17.125, 26.125 and 38.125 at k F , 3 k F , 5 k F , 7 k F and 9 k F . Our analytical results will provide insights into criticality in condensed matter physics.