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arXiv:cond-mat/9608114 · Physical review. B, Condensed matter

Variational state based on the Bethe-ansatz solution and a correlated singlet liquid state in the one-dimensionalt-Jmodel

Kenji Kobayashi, C. Ohe, Kaoru Iguchi

Published Nov 1, 1996• 4 citations
arXivHTMLPDF

Abstract

The one-dimensional t-J model is investigated by the variational Monte Carlo method. A variational wave function based on the Bethe-ansatz solution is proposed, where the spin-charge separation is realized and a long-range correlation factor of Jastrow-type is included. In most regions of the phase diagram, this wave function provides an excellent description of the ground-state properties characterized as a Tomonaga-Luttinger liquid; both the amplitude and exponent of correlation functions are correctly reproduced. For the spin-gap phase, another trial state of correlated singlet pairs with a Jastrow factor is introduced. This wave function shows generalized Luther-Emery-liquid behavior, exhibiting enhanced superconducting correlations and exponential decay of the spin correlation function. Using these two variational wave functions, the whole phase diagram is determined. In addition, relations between the correlation exponent and variational parameters in the trial functions are derived. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.13129

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The one-dimensional t-J model is investigated by the variational Monte Carlo method. A variational wave function based on the Bethe-ansatz solution is proposed, where the spin-charge separation is realized and a long-range correlation factor of Jastrow-type is included. In most regions of the phase diagram, this wave function provides an excellent description of the ground-state properties characterized as a Tomonaga-Luttinger liquid; both the amplitude and exponent of correlation functions are correctly reproduced. For the spin-gap phase, another trial state of correlated singlet pairs with a Jastrow factor is introduced. This wave function shows generalized Luther-Emery-liquid behavior, exhibiting enhanced superconducting correlations and exponential decay of the spin correlation function. Using these two variational wave functions, the whole phase diagram is determined. In addition, relations between the correlation exponent and variational parameters in the trial functions are derived. \textcopyright{} 1996 The American Physical Society.
We propose a correlated spin-singlet-pair wave function to describe the spin-gap phase of the one-dimensional t-J model at low density and large J/t. In addition to having singlet pairs, this wave function has a Jastrow factor with a variational parameter \ensuremath{\nu}. Several correlation functions are calculated by using the variational Monte Carlo method. The result shows the expected long-range behavior of the Luther-Emery phase with the Luttinger exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ related to \ensuremath{\nu}, ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$=1/2\ensuremath{\nu}. \textcopyright{} 1996 The American Physical Society.
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 study the t-J model in one dimension by numerically projecting the true ground state from a Luttinger-liquid trial wave function. We find the model exhibits Luttinger-liquid behavior for most of the phase diagram in which interaction strength and density are varied. However, at small densities and high interaction strengths a new phase with a gap to spin excitations and enhanced superconducting correlations is found. We show that this phase is a Luther-Emery liquid and study its correlation functions.
We present very general techniques for investigating strongly correlated lattice fermions in one dimension. We derive a variational wave function with a long ranged Jastrow factor that automatically satisfies the no double occupancy constraint present in many model Hamiltonians. The wave function is shown to be a generalized Luttinger liquid, and we use it to estimate ground state properties of the strongly correlated Hubbard model and the t-J model. We develop a numerical method to project the ground state from an arbitrary trial state. With the Luttinger liquid wave function as the initial guess, we calculate the exact ground state phase diagram of the t-J model. We discover a new phase in the model where Luttinger liquid behavior breaks down and superconducting correlations dominate the long range behavior of the system.
The phase diagram of the one-dimensional t-J model is investigated by analyzing the results of exact diagonalization and the exact solutions at J/t=0 and 2. Phase separation takes place above a critical value of J around Jc{\mathit{J}}_{\mathit{c}}Jc​/t=2.5--3.5 depending on the electron density. In the small-J region, Tomonaga-Luttinger liquid theory holds and its correlation exponents are calculated as a function of J/t and the electron density. Superconducting correlations become dominant in a region between the solvable case (J/t=2) and phase separation. A spin-gap region is also found at low density.
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.