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Journal of Experimental and Theoretical Physics

Ground state of Fermi systems with strong short-range order

Yu. B. Kudasov

Published Mar 1, 2000• 0 citations
Publisher

Abstract

A new variational method is developed to calculate the ground-state energy of a fermion system with strong short-range order. As well as intrasite correlations, the Gutzwiller trial wave function explicitly contains nearest-neighbor correlations. The Kikuchi pseudo-ensemble method was used to calculate the total energy of the fermion system. The calculations were made for the paramagnetic and antiferromagnetic phases of the half-filled Hubbard model. It is shown that for two-and three-dimensional lattices the short-range order in the paramagnetic phase strongly influences the ground-state energy whereas in the antiferromagnetic phase it is insignificant.

DOI
10.1134/1.559137

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A new variational method is developed to calculate the ground-state energy of a fermion system with strong short-range order. As well as intrasite correlations, the Gutzwiller trial wave function explicitly contains nearest-neighbor correlations. The Kikuchi pseudo-ensemble method was used to calculate the total energy of the fermion system. The calculations were made for the paramagnetic and antiferromagnetic phases of the half-filled Hubbard model. It is shown that for two-and three-dimensional lattices the short-range order in the paramagnetic phase strongly influences the ground-state energy whereas in the antiferromagnetic phase it is insignificant.
A new variational method is developed to calculate the ground state energy of Fermi systems with strong short-range correlations. A trial wave function of Gutzwiller's type contains additional variational parameters corresponding to configurations of pairs of nearest-neighbor sites. To evaluate the ground state energy, generalized Kikuchi's pseudo-ensemble method is used. The Hubbard model at half band-filling is investigated. The ground state energy of the paramagnetic phase is calculated for a chain, square and simple cubic lattices. It is shown that the short-range order lowers drastically the ground state energy of the Hubbard model at intermediate interaction strength. The paramagnetic phase of the Kondo-Hubbard model (S=1/2S=1/2S=1/2 and S=5/2S=5/2S=5/2) at half band-filling is investigated. The ground state energy, correlation functions and effective mass are calculated for chain, square and simple cubic lattices. A quantum phase transition was found for simple cubic lattice.
A new method is presented which allows for calculating the free energy of strongly correlated electrons. It makes use of projection techniques. The method is applied to calculate the ground-state energy of a (half-filled) two band Hubbard system in 2D. One term in it corresponds to the energy of a Heisenberg antiferromagnet. A number of trial wave functions are discussed for the latter system, with special emphasis given to a generalization of the Hulthen–Kasteleijn–Marshall wave function. Finally, we comment on the wave function when the ground state is a superconductor with strong short-range correlations.
We explore the phase diagram of the Hubbard model by generalizing the Gutzwiller variational wave function to take into account nearest-neighbor spin correlations. The energies of various variational states are calculated and compared. At half filling the lowest energy state has long-range antiferromagnetic correlations, in agreement with previous results. Away from half filling, when the antiferromagnet no longer has the lowest energy, the Gutzwiller approximation yields a lower energy than that found for small spin polarons.
By using the classic approximation method of Singwi, Tosi, Land, and Sj\"olander (STLS), we calculate the ground-state energy of the one- and two-dimensional Hubbard model in the half-filled antiferromagnetic state. In the one-dimensional case, by comparison with the exact result of Lieb and Wu, we find that the STLS correlation energy is generally better than that obtained from the random-phase approximation (RPA) and competes in quality with the best values obtained from variational calculations based on the antiferromagnetic Gutzwiller wave function (AFGWF). In particular, the STLS approximation yields a maximum in the absolute value of the correlation energy as a function of U, which is also found in the exact treatment, but not in the RPA. However, the numerical values of the STLS correlation energy are not as accurate as in the case of the uniform electron gas. In two dimensions, where the exact energy is not known, we find a similar relationship between the results of STLS, RPA, and AFGWF calculations, but the absolute value of the correlation energy is smaller. For large values of U, in both dimensions, the STLS method (like the RPA) runs into difficulties, due to the insufficient treatment of transverse spin fluctuations.
Recent refinements of analytical and numerical methods have improved our understanding of the ground-state phase diagram of the two-dimensional (2D) Hubbard model. Here, we focus on variational approaches, but comparisons with both quantum cluster and Gaussian Monte Carlo methods are also made. Our own ansatz leads to an antiferromagnetic ground state at half filling with a slightly reduced staggered order parameter (as compared to simple mean-field theory). Away from half filling, we find d-wave superconductivity, but confined to densities where the Fermi surface passes through the antiferromagnetic zone boundary (if hopping between both nearest-neighbour and next-nearest-neighbour sites is considered). Our results agree surprisingly well with recent numerical studies using the quantum cluster method. An interesting trend is found by comparing gap parameters Δ (antiferromagnetic or superconducting) obtained with different variational wave functions. Δ varies by an order of magnitude and thus cannot be taken as a characteristic energy scale. In contrast, the order parameter is much less sensitive to the degree of sophistication of the variational schemes, at least at and near half filling.
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.