1D half-filled paramagnetic Hubbard model.The Luttinger critical exponents

TL;DR

This paper analyzes the critical exponents of the 1D Hubbard model, revealing non-trivial low-energy behavior characteristic of Luttinger liquids, which differ significantly from Fermi liquid predictions.

Contribution

It provides a calculation of two key critical exponents that characterize the low-energy correlations in the 1D Hubbard model's Luttinger liquid phase.

Findings

Critical exponents differ from Fermi liquid predictions.

Density of states exhibits non-trivial power-law behavior.

Momentum distribution near $k_F$ shows Luttinger liquid characteristics.

Abstract

The electronic system of the 1D Hubbard model is not stable due to Peierls instability; the correlations are strong even for the weak Coulomb interaction. The resulting strongly correlated state without Landau quisi--particle excitations is known as the Luttinger liquid. Critical exponents of a power--law dependence of correlation functions at low energies differ substantially for the Luttinger and Fermi liquids. In this paper we evaluate two critical exponents that define non--trivial behavior of the density of electronic states at low frequences and the momentum distribution of the occupation number nearby $k_F$.