Application of the SD Technique for Solving a BCS-Reduced Hubbard  like Hamiltonian

We present exact and stochastic diagonalization results for a BCS-reduced Hubbard model. The kinetic Hamiltonian is the same as in the single band Hubbard model with additional next nearest neighbor hopping. The interaction of this model is designed to inhibit superconductivity in the d x2-y2 channel. The ground state of this model is studied by exact and stochastic diagonalization technique. We present a review of the technical details of the application of the stochastic diagonalization algorithm on this problem. To verify our results obtained with the stochastic diagonalization, they are compared with the exact diagonalization results. In order to show the convergence of the stochastic diagonalization we give a detailed analysis of the behavior of physical properties with increasing number of states. Finally we study superconductivity in this BCS-reduced Hubbard model. As an indicator of superconductivity we use the occurrence of Off Diagonal Long Range Order. We study the scaling behavior of this model for various attractive interactions and in addition the dependence of the superconducting correlation functions from the filling of the system.

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Off-Diagonal Long-Range Order in Generalized Hubbard Models

International Journal of Modern Physics B ◽

10.1142/s021797929700068x ◽

1997 ◽

Vol 11 (11) ◽

pp. 1311-1335 ◽

Cited By ~ 8

Author(s):

Kristel Michielsen ◽

Hans De Raedt

Keyword(s):

Density Matrix ◽

Hubbard Model ◽

Long Range ◽

Ground State ◽

Size Dependence ◽

State Energy ◽

System Size ◽

Range Order ◽

Long Range Order ◽

Hubbard Models

We present stochastic diagonalization results for the ground-state energy and the largest eigenvalue of the two-fermion density matrix of the BCS reduced Hamiltonian, the Hubbard model, and the Hubbard model with correlated hopping. The system-size dependence of this eigenvalue is used to study the existence of Off-Diagonal Long-Range Order in these models. We show that the model with correlated hopping and repulsive on-site interaction can exhibit Off-Diagonal Long-Range Order. Analytical results for some special limiting cases indicate that Off-Diagonal Long-Range Order not always implies superconductivity.

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GROUND STATE OF THE 2D EXTENDED HUBBARD MODEL WITH MORE THAN NEAREST-NEIGHBOR INTERACTIONS

International Journal of Modern Physics B ◽

10.1142/s0217979212501561 ◽

2012 ◽

Vol 26 (29) ◽

pp. 1250156 ◽

Cited By ~ 4

Author(s):

S. HARIR ◽

M. BENNAI ◽

Y. BOUGHALEB

Keyword(s):

Phase Diagram ◽

Hubbard Model ◽

Ground State ◽

State Energy ◽

Nearest Neighbor ◽

Finite Size ◽

Square Lattice ◽

Extended Hubbard Model ◽

Eigenvalues And Eigenvectors ◽

Repulsion Energy

We investigate the ground state phase diagram of the two dimensional Extended Hubbard Model (EHM) with more than Nearest-Neighbor (NN) interactions for finite size system at low concentration. This EHM is solved analytically for finite square lattice at one-eighth filling. All eigenvalues and eigenvectors are given as a function of the on-site repulsion energy U and the off-site interaction energy Vij. The behavior of the ground state energy exhibits the emergence of phase diagram. The obtained results clearly underline that interactions exceeding NN distances in range can significantly influence the emergence of the ground state conductor–insulator transition.

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TWO-DIMENSIONAL QUARTER-FILLED EXTENDED HUBBARD MODEL AT STRONG COUPLING

International Journal of Modern Physics B ◽

10.1142/s0217979205028256 ◽

2005 ◽

Vol 19 (01n03) ◽

pp. 213-216

Author(s):

W. F. LEE ◽

H. Q. LIN

Keyword(s):

Hubbard Model ◽

Correlation Functions ◽

Nearest Neighbor ◽

Spin Correlation ◽

Perturbation Approach ◽

Effective Hamiltonian ◽

Two Dimensional ◽

Extended Hubbard Model ◽

Neighbor Interaction ◽

Electron Hopping

In this paper, we generalized the perturbation approach to study the quasi-two-dimension extended Hubbard model. This model is characterizing by intra-chain electron hopping t, on-site Column interaction U, nearest-neighbor interaction V, and inter-chain electron hopping t′ and nearest-neighbor interaction V′. An effective Hamiltonian up to sixth-order in t/U, t/V, t/V′, t′/U, t′/V and t′/V′ expansion was obtained and the spin-spin correlation functions were calculated. We presented results for t=t′, V=V′.

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EFFECTS OF THE NEXT-NEAREST-NEIGHBOR HOPPING IN OPTICAL LATTICES

Modern Physics Letters B ◽

10.1142/s0217984908014572 ◽

2008 ◽

Vol 22 (01) ◽

pp. 33-44 ◽

Cited By ~ 4

Author(s):

YUN'E GAO ◽

FUXIANG HAN

Keyword(s):

Phase Diagram ◽

Hubbard Model ◽

Ground State Energy ◽

Ground State ◽

Optical Lattices ◽

State Energy ◽

Nearest Neighbor ◽

Three Dimensional ◽

Dispersion Relations ◽

Insulating Phase

Introducing the next-nearest-neighbor hopping t′ into the Bose–Hubbard model, we study its effects on the phase diagram, on the ground-state energy, and on the quasiparticle and quasihole dispersion relations of the Mott insulating phase in optical lattices. We have found that a negative value of t′ enlarges the Mott-insulating region on the phase diagram, while a positive value of t′ acts oppositely. We have also found that the effects of t′ are dependent on the dimensionality of optical lattices with its effects largest in three-dimensional optical lattices.

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Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model

Physical Review B ◽

10.1103/physrevb.96.075156 ◽

2017 ◽

Vol 96 (7) ◽

Cited By ~ 2

Author(s):

Mingpu Qin ◽

Hao Shi ◽

Shiwei Zhang

Keyword(s):

Hubbard Model ◽

Ground State ◽

Correlation Functions ◽

Short Range ◽

Spin Correlation ◽

Numerical Results ◽

Two Dimensional

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Exact-diagonalization study on the effect of the long-range Coulomb interaction to the superconducting ground state in the two-chain Hubbard model

Physica C Superconductivity ◽

10.1016/s0921-4534(98)00529-2 ◽

1998 ◽

Vol 308 (3-4) ◽

pp. 301-311 ◽

Cited By ~ 2

Author(s):

Soh Koike ◽

Kunihiko Yamaji ◽

Takashi Yanagisawa

Keyword(s):

Hubbard Model ◽

Long Range ◽

Coulomb Interaction ◽

Ground State ◽

Exact Diagonalization

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Exact demonstration of off-diagonal long-range order in the ground state of a Hubbard model

Physical Review Letters ◽

10.1103/physrevlett.71.4238 ◽

1993 ◽

Vol 71 (25) ◽

pp. 4238-4240 ◽

Cited By ~ 45

Author(s):

Shun-Qing Shen ◽

Zhao-Ming Qiu

Keyword(s):

Hubbard Model ◽

Long Range ◽

Ground State ◽

Range Order ◽

Long Range Order

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Study of correlation functions in molecular crystals

Canadian Journal of Physics ◽

10.1139/p89-181 ◽

1989 ◽

Vol 67 (11) ◽

pp. 1036-1039

Author(s):

M. S. Wartak ◽

C. Y. Fong

Keyword(s):

Correlation Function ◽

High Temperature ◽

Hubbard Model ◽

Correlation Functions ◽

Nearest Neighbor ◽

High Temperature Superconductors ◽

Molecular Crystals ◽

Vibrational Properties ◽

Model Hamiltonian

We have studied the correlation functions for a model Hamiltonian describing the vibrational properties in molecular crystals. The model Hamiltonian consists of terms characterizing the on-site anharmonicity and the nearest-neighbor hopping interaction. If the on-site anharmonicity is uniform, the correlation functions exhibit no structure. However, structure appears in the nearest-neighbor correlation function if the anharmonicity is nonuniform. Because the Hamiltonian resembles the Hubbard model for the electronic case, the implication of the results to high temperature superconductors is indicated.

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