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ANALYTIC CALCULATION OF GROUND-STATE PROPERTIES OF THE ONE-DIMENSIONAL T-J MODEL WITH A MODIFIED GUTZWILLER WAVE-FUNCTION

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Published Sep 10, 2026• 0 citations
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Abstract

An effective Hamiltonian equivalent to the t-J model is derived. We calculate analytically the ground-state energy and correlation functions for a modified Gutzwiller wave function using the technique developed by Metzner, Vollhardt, and Gebhard. We obtain results that are significantly better than those for the usual Gutzwiller wave function, and that are close to the exact results in some cases.

DOI
10.82444/warw.33552973

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Japanese Journal of Applied Physics•Jan 1, 1987•0 citations
An effective Hamiltonian equivalent to the t-J model is derived. We calculate analytically the ground-state energy and correlation functions for a modified Gutzwiller wave function using the technique developed by Metzner, Vollhardt, and Gebhard. We obtain results that are significantly better than those for the usual Gutzwiller wave function, and that are close to the exact results in some cases.
A new analytic approach to the evaluation of ground-state properties of Hubbard-type models in terms of the Gutzwiller variational wave function is presented. It is based on the observation that expectation values in terms of this wave function may be expressed by sums over different lattice sites. This makes the application of Wick's theorem and the resulting contractions extremely simple, since the latter involve only anticommuting numbers as in a Grassmann algebra. Expressions for the momentum distribution ${n}_{\mathrm{k}\ensuremath{\sigma}}$ and the Hubbard interaction in terms of a power series in a particular correlation parameter are derived which are valid for all dimensions. An explicit diagrammatic evaluation of the coefficients is described. In one dimension these coefficients may be determined to all orders which yields an approximation-free calculation of nk{n}_{\mathrm{k}}nk​ and ground-state energy E for arbitrary density n and interaction strength U. In the case of a half-filled band and large U, hitherto unexpected nonanalyticities are found. The results allow for the first approximation-free assessment of the properties of the Gutzwiller wave function. It is shown that the well-known Gutzwiller approximation may be derived diagrammatically, too. The approximation is seen to yield the exact results for expectation values in terms of this wave function in the limit of infinite dimensionality.
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 properties of the Gutzwiller variational wave function, which is frequently used to study ground-state properties of correlated fermions with a short-range interaction, are investigated by use of a new, analytically tractable approach. As a first application several ground-state quantities are evaluated exactly in dimensionality d=1 for arbitrary band-filling and interaction strengths. The results allow for the first approximation-free assessment of the wave function. The method itself is applicable to arbitrary space dimensions.