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Revista Mexicana de Física

Apareamiento electronico en el hamiltoniano de hubbard extendido

Oracio Navarro, C.H Wang

Published Jan 1, 1992• 3 citations
OpenAlex

Abstract

In this paper we report a novel method to find the exact solution oC the extended lIubbard lIamiltonian. This method is based on mapping the original problem onto a tight-binding probJem in a higher dimensional space, which has exact solution. For one- and two-dimensional systems with a low electronic density, we have calculated the electronic pairing energy and the coherence length Cor different interaction regimes. This study can be extended to analyze the electronie correlation in non-periodic systems.

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The local-pairing problem of two electrons with parallel and anti-parallel spins is analysed by looking at the pairing energy, the coherence length and the mobility of pairs in a square lattice. These physical quantities are calculated by a novel method based on mapping the Hubbard problem onto a tight-binding one in a higher-dimensional space, which can be solved exactly.

Journal of Physics Condensed Matter•Aug 16, 1993•0 citations

Two-particle correlations in the-dimensional hubbart model: a ground-state analytical solution

Emmanuel Vallejo, Oracio Navarro, José Eduardo Espinosa

SE RESOLVIO EL HAMILTONIANO DE HUBBARD EXTENDIDO PARA DOS PARTICULAS EN UNA RED UNIDIMENSIONAL, USANDO EL METODO DEL MAPEO EN EL ESPACIO REAL Y LA TECNICA DE LA FUNCION DE GREEN. ESTE HAMILTONIANO CONSIDERA LAS INTERACCIONES INTRA-ATOMICAS U E INTER-ATOMICAS V . EL METODO MAPEA EL PROBLEMA DE MUCHOS CUERPOS CORRELACION DE UN PROBLEMA EQUIVALENTE DE AMARRE FUERTE EN UN ESPACIO DE MAYOR DIMENSION. HACIENDO UN ANALISIS DEL PROBLEMA EN ESTE ESPACIO SE OBTUVO LA SOLUCION ANALITICA PARA LA ENERGIA DE ENLACE DEL ESTADO BASE. LOS RESULTADOS ESTAN EN COMPLETO ACUERDO CON LA SOLUCIONES OBTENIDAS TANTO NUMERICAMENTE [1] COMO EN EL ESPACIO RECIPROCO [2]. Abstract A SOLUTION TO THE EXTENDED HUBBARD HAMILTONIAN FOR THE CASE OF TWO-PARTICLES IN AN INFINITE ONE-DIMENSIONAL LATTICE IS PRESENTED, USING A REAL-SPACE MAPPING METHOD AND THE GREEN FUNCTION TECHNIQUE. THIS HAMILTONIAN CONSIDERS THE ON-SITE (U) AND THE NEAREST-NEIGHBOR (V ) INTERACTIONS. THE METHOD IS BASED ON MAPPING THE CORRELATED MANY-BODY PROBLEM ONTO AN EQUIVALENT SITE-IMPURITY TIGHT-BINDING ONE IN A HIGHER DIMENSIONAL SPACE. IN THIS NEW SPACE WE OBTAINED THE ANALYTICAL SOLUTION FOR THE GROUND STATE BINDING ENERGY. RESULTS ARE IN AGREEMENT WITH THE NUMERICAL SOLUTION OBTAINED PREVIOUSLY [1], AND WITH THOSE OBTAINED IN THE RECIPROCAL SPACE [2].

Revista Mexicana de Física•Jun 1, 2003•0 citations

Hubbard model in one dimension with a general bond-charge interaction: Analytical ground-state solution for the pairing of two particles

Emmanuel Vallejo, Oracio Navarro

In this work we solve a general Hubbard Hamiltonian for two interacting particles in a periodic and nonperiodic infinite one-dimensional lattice, using a real-space mapping method, the renormalized perturbation expansion (RPE), and the Green-function technique. This Hamiltonian considers a general bond-charge interaction, the on-site interaction, and the general intersite interaction. The real-space method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding problem in a higher-dimensional space. Analyzing the periodic and the quasiperiodic lattices in this new space, we obtained the analytical solution for the binding condition at the ground state. Our general results for the periodic chain reproduce completely the limit cases of the numerical solution obtained previously and those obtained in reciprocal space

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A density-functional theory for many-body lattice models is considered in which the single-particle density matrix ${\ensuremath{\gamma}}_{\mathrm{ij}}$ is the basic variable. Eigenvalue equations are derived for solving Levy's constrained search of the interaction energy functional $W[{\ensuremath{\gamma}}_{\mathrm{ij}}].$ $W[{\ensuremath{\gamma}}_{\mathrm{ij}}]$ is expressed as the sum of Hartree-Fock energy ${E}_{\mathrm{HF}}[{\ensuremath{\gamma}}_{\mathrm{ij}}]$ and the correlation energy ${E}_{C}[{\ensuremath{\gamma}}_{\mathrm{ij}}].$ Exact results are obtained for ${E}_{C}({\ensuremath{\gamma}}_{12})$ of the Hubbard model on various periodic lattices, where ${\ensuremath{\gamma}}_{\mathrm{ij}}={\ensuremath{\gamma}}_{12}$ for all nearest neighbors i and j. The functional dependence of ${E}_{C}({\ensuremath{\gamma}}_{12})$ is analyzed by varying the number of sites ${N}_{a},$ band filling ${N}_{e},$ and lattice structure. The infinite one-dimensional chain and one-, two-, or three-dimensional finite clusters with periodic boundary conditions are considered. The properties of ${E}_{C}({\ensuremath{\gamma}}_{12})$ are discussed in the limits of weak $({\ensuremath{\gamma}}_{12}\ensuremath{\simeq}{\ensuremath{\gamma}}_{12}^{0})$ and strong $({\ensuremath{\gamma}}_{12}\ensuremath{\simeq}{\ensuremath{\gamma}}_{12}^{\ensuremath{\infty}})$ electronic correlations, and in the crossover region $({\ensuremath{\gamma}}_{12}^{\ensuremath{\infty}}<~{\ensuremath{\gamma}}_{12}<~{\ensuremath{\gamma}}_{12}^{0}).$ Using an appropriate scaling we observe that ${\ensuremath{\varepsilon}}_{C}{(g}_{12}{)=E}_{C}{/E}_{\mathrm{HF}}$ has a pseudo-universal behavior as a function of ${g}_{12}=({\ensuremath{\gamma}}_{12}\ensuremath{-}{\ensuremath{\gamma}}_{12}^{\ensuremath{\infty}})/({\ensuremath{\gamma}}_{12}^{0}\ensuremath{-}{\ensuremath{\gamma}}_{12}^{\ensuremath{\infty}}).$ The fact that ${\ensuremath{\varepsilon}}_{C}{(g}_{12})$ depends weakly on ${N}_{a},$ ${N}_{e},$ and lattice structure suggests that the correlation energy of extended systems could be obtained quite accurately from finite-cluster calculations. Finally, the behaviors of ${E}_{C}({\ensuremath{\gamma}}_{12})$ for repulsive $(U>0)$ and attractive $(U<0)$ interactions are contrasted.

arXiv:cond-mat/9910264•Physical review. B, Condensed matter•Jan 15, 2000•45 citations

The exact diagonalization of the extended Hubbard Model: Six Electrons at Half-Filling

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This study has used the exact diagonalization technique to examine the Extended Hubbard model.The basis vectors were first generated using binary integers available in matlab,the Hamiltonian matrix were subsequently generated using the basis vectors,after-which the Eigen values of the low and some highest laying states were obtained. The results obtained would serve as a good reference against which other results obtained from other approximation techniques can be compared .

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Hubbard model with next-nearest-neighbour interaction terms in higher dimensions: New, exactly solvable cases

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The exact ground-state wavefunction and energy of an extended Hubbard model are presented containing also next-nearest-neighbour hopping, bond-charge and density interaction terms besides the nearest-neighbour and on-site contributions. Our results are valid at half-filling for a wide range of parameters, on simple hypercubic lattices in arbitrary D > I dimensions.

Philosophical Magazine B•Nov 1, 1997•2 citations
In this paper we report a novel method to find the exact solution oC the extended lIubbard lIamiltonian. This method is based on mapping the original problem onto a tight-binding probJem in a higher dimensional space, which has exact solution. For one- and two-dimensional systems with a low electronic density, we have calculated the electronic pairing energy and the coherence length Cor different interaction regimes. This study can be extended to analyze the electronie correlation in non-periodic systems.
SE RESOLVIO EL HAMILTONIANO DE HUBBARD EXTENDIDO PARA DOS PARTICULAS EN UNA RED UNIDIMENSIONAL, USANDO EL METODO DEL MAPEO EN EL ESPACIO REAL Y LA TECNICA DE LA FUNCION DE GREEN. ESTE HAMILTONIANO CONSIDERA LAS INTERACCIONES INTRA-ATOMICAS U E INTER-ATOMICAS V . EL METODO MAPEA EL PROBLEMA DE MUCHOS CUERPOS CORRELACION DE UN PROBLEMA EQUIVALENTE DE AMARRE FUERTE EN UN ESPACIO DE MAYOR DIMENSION. HACIENDO UN ANALISIS DEL PROBLEMA EN ESTE ESPACIO SE OBTUVO LA SOLUCION ANALITICA PARA LA ENERGIA DE ENLACE DEL ESTADO BASE. LOS RESULTADOS ESTAN EN COMPLETO ACUERDO CON LA SOLUCIONES OBTENIDAS TANTO NUMERICAMENTE [1] COMO EN EL ESPACIO RECIPROCO [2]. Abstract A SOLUTION TO THE EXTENDED HUBBARD HAMILTONIAN FOR THE CASE OF TWO-PARTICLES IN AN INFINITE ONE-DIMENSIONAL LATTICE IS PRESENTED, USING A REAL-SPACE MAPPING METHOD AND THE GREEN FUNCTION TECHNIQUE. THIS HAMILTONIAN CONSIDERS THE ON-SITE (U) AND THE NEAREST-NEIGHBOR (V ) INTERACTIONS. THE METHOD IS BASED ON MAPPING THE CORRELATED MANY-BODY PROBLEM ONTO AN EQUIVALENT SITE-IMPURITY TIGHT-BINDING ONE IN A HIGHER DIMENSIONAL SPACE. IN THIS NEW SPACE WE OBTAINED THE ANALYTICAL SOLUTION FOR THE GROUND STATE BINDING ENERGY. RESULTS ARE IN AGREEMENT WITH THE NUMERICAL SOLUTION OBTAINED PREVIOUSLY [1], AND WITH THOSE OBTAINED IN THE RECIPROCAL SPACE [2].
In this work we solve a general Hubbard Hamiltonian for two interacting particles in a periodic and nonperiodic infinite one-dimensional lattice, using a real-space mapping method, the renormalized perturbation expansion (RPE), and the Green-function technique. This Hamiltonian considers a general bond-charge interaction, the on-site interaction, and the general intersite interaction. The real-space method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding problem in a higher-dimensional space. Analyzing the periodic and the quasiperiodic lattices in this new space, we obtained the analytical solution for the binding condition at the ground state. Our general results for the periodic chain reproduce completely the limit cases of the numerical solution obtained previously and those obtained in reciprocal space
A density-functional theory for many-body lattice models is considered in which the single-particle density matrix ${\ensuremath{\gamma}}_{\mathrm{ij}}$ is the basic variable. Eigenvalue equations are derived for solving Levy's constrained search of the interaction energy functional $W[{\ensuremath{\gamma}}_{\mathrm{ij}}].$ $W[{\ensuremath{\gamma}}_{\mathrm{ij}}]$ is expressed as the sum of Hartree-Fock energy ${E}_{\mathrm{HF}}[{\ensuremath{\gamma}}_{\mathrm{ij}}]$ and the correlation energy ${E}_{C}[{\ensuremath{\gamma}}_{\mathrm{ij}}].$ Exact results are obtained for ${E}_{C}({\ensuremath{\gamma}}_{12})$ of the Hubbard model on various periodic lattices, where ${\ensuremath{\gamma}}_{\mathrm{ij}}={\ensuremath{\gamma}}_{12}$ for all nearest neighbors i and j. The functional dependence of ${E}_{C}({\ensuremath{\gamma}}_{12})$ is analyzed by varying the number of sites Na,{N}_{a},Na​, band filling Ne,{N}_{e},Ne​, and lattice structure. The infinite one-dimensional chain and one-, two-, or three-dimensional finite clusters with periodic boundary conditions are considered. The properties of ${E}_{C}({\ensuremath{\gamma}}_{12})$ are discussed in the limits of weak $({\ensuremath{\gamma}}_{12}\ensuremath{\simeq}{\ensuremath{\gamma}}_{12}^{0})$ and strong $({\ensuremath{\gamma}}_{12}\ensuremath{\simeq}{\ensuremath{\gamma}}_{12}^{\ensuremath{\infty}})$ electronic correlations, and in the crossover region $({\ensuremath{\gamma}}_{12}^{\ensuremath{\infty}}<~{\ensuremath{\gamma}}_{12}<~{\ensuremath{\gamma}}_{12}^{0}).$ Using an appropriate scaling we observe that ${\ensuremath{\varepsilon}}_{C}{(g}_{12}{)=E}_{C}{/E}_{\mathrm{HF}}$ has a pseudo-universal behavior as a function of ${g}_{12}=({\ensuremath{\gamma}}_{12}\ensuremath{-}{\ensuremath{\gamma}}_{12}^{\ensuremath{\infty}})/({\ensuremath{\gamma}}_{12}^{0}\ensuremath{-}{\ensuremath{\gamma}}_{12}^{\ensuremath{\infty}}).$ The fact that ${\ensuremath{\varepsilon}}_{C}{(g}_{12})$ depends weakly on Na,{N}_{a},Na​, Ne,{N}_{e},Ne​, and lattice structure suggests that the correlation energy of extended systems could be obtained quite accurately from finite-cluster calculations. Finally, the behaviors of ${E}_{C}({\ensuremath{\gamma}}_{12})$ for repulsive (U>0)(U>0)(U>0) and attractive (U<0)(U<0)(U<0) interactions are contrasted.