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Physica Scripta

Electron correlations in two dimensions

K. W. Becker, Peter Fulde

Published Jan 1, 1989• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/1989/t27/019

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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.
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 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.
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.
PACS. 71.10.−w – Theories and models of many electron systems. PACS. 71.10.Fd – Lattice fermion models. PACS. 71.15.Th – Other methods. Abstract. – The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions, which cannot be obtained by means of the Bethe Ansatz, except for some limiting cases. Introduction. – New materials whose physics is dominated by electron correlations in narrow energy bands are actually a challenge for solid state physicists. The treatment of such systems is not trivial due to the competition between itinerant and localized behaviour of the electrons in these bands. The Hubbard Hamiltonian [1] is regarded as the simplest model
A recently proposed projection operator technique based on the introduction of cumulants is used to investigate the ground-state energy of the Hubbard model at half filling on a square lattice in two dimensions, in the antiferromagnetic phase. Our results in the intermediate and large regime of the ratio U/t are below those of variational Monte Carlo calculations, which set an upper bound for the energy. By including the most dominant spin-fluctuation processes, the present calculation also obeys the correct infinite U/t limit, where the Hubbard model at half filling reduces to the Heisenberg antiferromagnet. The relation of our approach to recent coupled-cluster calculations for the Hubbard model is also discussed. \textcopyright{} 1996 The American Physical Society.
The authors have analysed finite clusters with different degrees of frustration on the basis of the conventional Hubbard model. In particular they have calculated the ground-state energy and certain correlation functions as a function of the interaction energy U. As U varies, a sharp transition is observed between two different structures for half-filled bands. The authors have studied these clusters not only for the case of a half-filled band but also for different numbers of holes. They found that the structure of the ground state depends critically on the total spin and the number of holes.