Renormalization-group acceleration of self-consistent field solutions: Two-dimensional Hubbard model

1994 ◽  
Vol 49 (3) ◽  
pp. 1586-1599 ◽  
Author(s):  
Chien-Hua Pao ◽  
N. E. Bickers
Keyword(s):  
Renormalization Group ◽  
Hubbard Model ◽  
Two Dimensional ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

Determining the Morphology and the Interaction Between Terminally-Anchored Polymer Layers

1996 ◽  
Vol 461 ◽  
Author(s):  
A. C. Balazs ◽  
C. Singh
Keyword(s):  
Field Theory ◽  
Colloidal Particles ◽  
The Other ◽  
Two Dimensional ◽  
Planar Surfaces ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Energy Of Interaction ◽  
Self Consistent Field Theory

ABSTRACTUsing a two dimensional self-consistent field theory, we investigate the interactions between two planar surfaces that are coated with terminally-anchored homopolymers. One surface is coated with A chains and the other is covered with B homopolymers. The chains are grafted at low densities and the B polymers are chosen to be solvophobic, while the A chains are relatively solvophilic. We determine the morphology of the layers and the energy of interaction asthe surfaces are compressed. Our results provide guidelines for controlling the interaction between polymer-coated colloidal particles.

Pertubation Theory About Self-Consistent Field Solution in One-Dimensional Hubbard Model

2003 ◽  
Vol 17 (18n20) ◽  
pp. 3363-3366 ◽  
Author(s):  
A. N. Kocharian ◽  
C. Yang ◽  
Y. L. Chiang
Keyword(s):  
Perturbation Theory ◽  
Hubbard Model ◽  
Electron Concentration ◽  
Ground State ◽  
Second Order ◽  
Electron Interaction ◽  
Field Solution ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

The accurate analytical and numerical calculations of the electronic band structure and ground state properties of strongly correlated electrons within the Hubbard model are performed by constructing convergent perturbation theory for general interaction strength and electron concentration. We test the developed perturbation approach about mean field solution in the extreme conditions of one dimensionality for entire parameter space of electron interaction U/t and electron concentration n. The many-body perturbation formalism up two second order about the generalized self-consistent field (GSCF) Hamiltonian goes beyond the range of applicability of standard perturbation theory by incorporating systematically the effect of the random-phase-type perturbation techniques and controlled expansion of the energy functional for general U/t and n. The second order perturbation correction vanishes at small and large U/t limit and performed calculations of the ground state energy show a next to the perfect numerical agreement with the Bethe-ansatz results.

CALCULATIONS OF THE MEAN SQUARE RELATIVE ATOMIC DISPLACEMENTS IN A SIMPLE MODEL OF AN ANHARMONIC CRYSTAL

1995 ◽  
Vol 09 (23) ◽  
pp. 1513-1519
Author(s):  
M. F. PASCUAL ◽  
V. I. ZUBOV
Keyword(s):  
Square Lattice ◽  
Mean Square ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Anharmonic Crystal ◽  
Atomic Displacements ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The Mean

We have used the correlative method of unsymmetrized self-consistent field to calculate the mean square relative displacements (MSRD) of atoms in the two-dimensional model of the anharmonic crystal with square lattice. The longitudinal and transversal components of MSRD between the nearest, second, third and next neighbors have been computed. An influence of the anharmonicity on various components as well as peculiarities of the lattice considered are discussed.

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