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Physical Review Letters

Variational wave functions and ground-state properties in the one-dimensionalt-Jmodel

Hisatoshi Yokoyama, Masao Ogata

Published Dec 16, 1991• 36 citations
Publisher

Abstract

Ground-state properties of the one-dimensional t-J model are studied by using exact diagonalization of small systems and compared with those found with Gutzwiller-Jastrow--type variational functions. Near the supersymmetric case (J/t=2), the Gutzwiller wave function is an extremely good trial function for all electron densities. It reproduces momentum distribution and correlation functions of the exact ground state except for critical behaviors. For J/t2 (>2), the ground-state properties are well described by Jastrow functions with repulsive (attractive) intersite correlations.

DOI
10.1103/physrevlett.67.3610

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Ground-state properties of the one-dimensional t-J model are studied by using exact diagonalization of small systems and compared with those found with Gutzwiller-Jastrow--type variational functions. Near the supersymmetric case (J/t=2), the Gutzwiller wave function is an extremely good trial function for all electron densities. It reproduces momentum distribution and correlation functions of the exact ground state except for critical behaviors. For J/t2 (>2), the ground-state properties are well described by Jastrow functions with repulsive (attractive) intersite correlations.
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.
Two-dimensional t-J model is studied by a variational Monte Carlo method, using Gutzwiller-Jastrow-type wave functions. Various kinds of superconducting pairing symmetries are compared in order to determine the phase diagram of the ground state in the full J/t-n plane. Near the half filling where the high temperature superconductivity is expected, the d_{x^2-y^2} wave pairing state is always the most stable among various symmetries. The three-site term hardly changes the phase diagram in this regime. In the low electron density, the extended s-type wave becomes a quantitatively good state for large J/t, although the energy gain is small. The Gutzwiller wave function is shown to be the exact ground state in the low-electron-density limit for the supersymmetric case (J/t=2).
New variational wave functions are introduced to describe the Hubbard model in strong correlation. Intersite correlation (or Jastrow) factors are taken into account beyond the Gutzwiller wave function (GF). A study is made on the one-dimensional lattice and the two-dimensional square lattice at half-filling as well as less-than-half-filling. Much improvement can be achieved thereby in the description of physical quantities such as the momentum distribution and spin and charge density correlation functions. In addition, the ground state energy is lowered appreciably compared with the GF. In this connection, the Mott-Hubbard-type metal-insulator transition is also re-examined.
We find the Gutzwiller projected Fermi sea wave function(GWF) has the correct phase structure to describe the kink nature of the doped holes in the ground state of the one dimensional t−Jt-Jt−J model. We find the failure of the GWF for general value of J/tJ/tJ/t and electron density nnn can be attributed to the residual charge correlation in the ground state. We find such residual charge correlation is well described by a XXZ-type effective Hamiltonian. Based on these observations, a Pfaffian-type variational wave function is proposed and is found to reproduce correctly the global phase diagram and corresponding correlation functions of the one dimensional t−Jt-Jt−J model, including the Luther-Emery phase in the low electron density and large J/tJ/tJ/t region.
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.