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Physical review. B, Condensed matter

Electron correlations in the ground state of diamond from the projection technique

Dadong Yan, Tran Minh-Tien

Published Aug 15, 1999• 0 citations
Publisher

Abstract

We calculate the ground-state energy of a diamondlike structure for a Hamiltonian which includes kinetic energy, Coulomb interaction, and exchange interaction between neighboring bonds. Our aim is to study the case of increasing lattice constants which leads to a crossover from weak to strong correlations in diamond. Eventually the system goes over into one of free atoms. Starting from the ansatz of exponential form, we use the projection techniques combined with a cumulant formalism to obtain the ground-state energy.

DOI
10.1103/physrevb.60.4587

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We calculate the ground-state energy of a diamondlike structure for a Hamiltonian which includes kinetic energy, Coulomb interaction, and exchange interaction between neighboring bonds. Our aim is to study the case of increasing lattice constants which leads to a crossover from weak to strong correlations in diamond. Eventually the system goes over into one of free atoms. Starting from the ansatz of exponential form, we use the projection techniques combined with a cumulant formalism to obtain the ground-state energy.
Abstract Recently, it has been shown that the ground‐state energy of a quantum many‐body system can be written in terms of cumulants. In this article, we show that the energies of excited states can be expressed similarly. These representations are suitable for various approximation schemes, e.g., projection techniques. The explicit use of cumulants ensures size consistency in all approximations. The theory is then applied to the computation of the energy bands of a semiconductor with a diamond structure. As we focus especially on the effects of electron correlations, we consider a simplified model and rederive results obtained previously by the variational local ansatz method. © 1994 John Wiley & Sons, Inc.
Abstract A systematic nonperturbative scheme for calculating the ground state energy is adapted for studying systems of strongly correlated electrons on a lattice. It includes a method for calculating the cumulants of the Hamiltonian and a method, using the t-expansion, for constructing successive approximations to the ground state energy by these cumulants. The scheme is applied to spinless fermion and Hubbard models, and a method is proposed to overcome the problems found in previous attempts to use this scheme to study the Hubbard model.
The ground state of the two-dimensional (2D) Hubbard model is investigated by adopting improved wave functions that take into account intersite electron correlation beyond the Gutzwiller ansatz. The ground-state energy is lowered considerably, giving the best estimate of the ground-state energy for the 2D Hubbard model. There is a crossover from weakly to strongly correlated regions as the on-site Coulomb interaction UUU increases. The antiferromagnetic correlation induced by UUU is reduced for hole doping when UUU is large, being greater than the bandwidth, thus increasing the kinetic energy gain. The spin and charge fluctuations are induced in the strongly correlated region. These antiferromagnetic and kinetic charge fluctuations induce electron pairings, which would result in high-temperature superconductivity.
By applying projection techniques a unified description of weakly and strongly correlated electronic systems can be given. For that purpose the theory is formulated in Liouville instead of Hilbert space. By introducing an appropriate metric in terms of cumulants it is ensured that all energies are size consistent. An energy expression is derived which is a generalization of Goldstone’s linked cluster theorem for arbitrary Hamiltonians. It is suitable for applying the projection method of Zwanzig and Mori. The equations for the correlation energy within the Local Ansatz and within coupled electron pair approximation CEPA-2 follow straightforwardly from the present theory.
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.
Various methods and approximation schemes are used to study many-electron interacting systems. Two important many-particle models, the Anderson model and the Hubbard model, and their electromagnetic properties have been investigated in many parameter regimes, and applied to physical systems. An Anderson single-impurity model Hamiltonian based calculation of the magnetic susceptibility is performed for YbN in the presence of crystal fields using an alteration of the Non-Crossing Approximation proposed by Zwicknagl et.al., incorporating parameters obtained from ab initio band structure calculations. It yields good agreement with experimental data. For the Anderson lattice model, a variational scheme which uses specific many-electron wavefunctions as basis is applied to both one- and two-dimensional systems represented by symmetric Anderson lattice Hamiltonians. Without much computational effort, the ground state energy is well approximated, especially in strong-coupling limit. Some electronic properties are examined using the variational ground state wavefunction. The one-dimensional Hubbard model has been solved exactly for small-size clusters by diagonalizing the Hamiltonian in the basis of many-electron Bloch states. The results for the energy spectrum and eigenfunctions of the ground state and low-lying excited states are presented. Also, mean field calculations of the two-dimensional single-band Hubbard model and Cu-O lattice model (three-band Hubbard model) are carried out for various physical quantities including the energy, occupation probability, staggered magnetization, momentum distribution Fermi surface and density of states, by using a projection operator formalism. To develop a systematic approach to solving many-electron problems, the many-particle partition function for the free electron gas system is explored using a cumulant expansion scheme. Starting from the ground state, the partition function can be approximated to any order in terms of excitation energy. Its application to interacting systems such as the Anderson model and the Hubbard model is briefly discussed.