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

Manuela Capello·Federico Becca·Seiji Yunoki·Michele Fabrizio·Sandro Sorella
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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.

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Manuela Capello, Federico Becca, Seiji Yunoki, Michele Fabrizio, Sandro Sorella. 2005-05-30. From Luttinger liquid to Mott insulator: the correct low-energy description of the one-dimensional Hubbard model by an unbiased variational approach. https://doi.org/10.1103/physrevb.72.085121

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