From Luttinger liquid to Mott insulator: the correct low-energy description of the one-dimensional Hubbard model by an unbiased variational approach

TL;DR

This paper introduces an unbiased variational wave function approach that accurately captures the low-energy physics of the one-dimensional Hubbard model, including the transition from a Luttinger liquid to a Mott insulator, without assuming specific parametric forms.

Contribution

The authors develop a generalized variational wave function that reproduces the Hubbard model's low-energy properties and captures the continuous transition from conducting to insulating phases.

Findings

Correct power-law correlation functions in the conducting phase.

Continuous change in the Jastrow factor at the insulator transition.

Accurate description of the Luttinger-liquid behavior and Mott insulator transition.

Abstract

We show that a particular class of variational wave functions reproduces the low-energy properties of the Hubbard model in one dimension. Our approach generalizes to finite on-site Coulomb repulsion the fully-projected wave function proposed by Hellberg and Mele [Phys. Rev. Lett. {\bf 67}, 2080 (1991)] for describing the Luttinger-liquid behavior of the doped $t{-}J$ model. Within our approach, the long-range Jastrow factor emerges from a careful minimization of the energy, without assuming any parametric form for the long-distance tail. Specifically, in the conducting phase of the Hubbard model at finite hole doping, we obtain the correct power-law behavior of the correlation functions, with the exponents predicted by the Tomonaga-Luttinger theory. By decreasing the doping, the insulating phase is reached with a continuous change of the small-$q$ part of the Jastrow factor.