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arXiv:cond-mat/0604492

The Hellberg-Mele Jastrow factor as a variational wave function for the one dimensional XXZ model

Hong-Yu Yang, Tao Li

Published Apr 20, 2006• 0 citations
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Abstract

We find the Jastrow factor introduced by Hellberg and Mele in their study of the one dimensional t-J model provides an exceedingly good variational description of the one dimensional XXZ model.
DOI
10.48550/arxiv.cond-mat/0604492

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The one-dimensional (1D) t-J model is investigated by using a Gutzwiller-Jastrow-type variation method and the exact diagonalization of small systems. Variational expectation values are estimated by the variational Monte Carlo method with sufficient accuracy. First, we give detailed descriptions of the preceding paper [Phys. Rev. Lett. 67, 3610 (1991)], where we discussed the properties of the Fermi-liquid-type Jastrow wave function as well as the Gutzwiller wave function. Secondly, these wave functions are compared with the Tomonaga-Luttinger-liquid-type wave function proposed by Hellberg and Mele. It is found that the correlation factors in short distances control bulk quantities like energy and the magnitude of the correlation functions, while the long-range part of the correlation factors determines the critical behavior of correlation functions. Finally, using these functions, charge, spin susceptibilities, and magnetization curve are estimated, which agree with the exact results. It is shown that the Mott transition in the 1D t-J model is quite different from the Brinkman-Rice transition. \textcopyright{} 1996 The American Physical Society.
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. 67, 2080 (1991)] for describing the Luttinger-liquid behavior of the doped $t\ensuremath{-}J$ 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 correlations, 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-qqq part of the Jastrow factor.