Reconstructions and Morphological Instabilities of FCC (110)Surfaces

1991 ◽  
Vol 229 ◽  
Author(s):  
J. Sun ◽  
Craig Rottman
Keyword(s):  
Phase Diagram ◽  
Ground State ◽  
Lattice Model ◽  
State Energy ◽  
Flat Surface ◽  
Pair Potential ◽  
Embedded Atom Method ◽  
Embedded Atom ◽  
Three Body ◽  
Pair And Triplet Interactions

AbstractWe compare the ground state energy of the following structures of fcc (110) surfaces: the (1×1) flat surface, the (n×1) reconstruction (2 ≤ n < ∞), and the (∞ × 1) structure where the surface is faceted into macroscopic (111) surfaces. We map out the phase diagram using a lattice model with pair and triplet interactions. We argue that it is unlikely that any realist pair potential will give a reconstructed ground state. We also doubt that including, in addition, three body interactions will stabilize the reconstructed structure for interatomic interactions derived from the embedded atom method.

THE ANGULAR MOMENTUM DEPENDENT CALCULATION OF THE GROUND STATE ENERGY OF LIQUID 3He

2005 ◽  
Vol 19 (30) ◽  
pp. 1793-1802 ◽  
Author(s):  
M. MODARRES
Keyword(s):  
Angular Momentum ◽  
Ground State Energy ◽  
Ground State ◽  
Correlation Functions ◽  
State Energy ◽  
Interatomic Potentials ◽  
Channel Correlation ◽  
P Waves ◽  
Effective Interactions ◽  
Three Body

We investigate the possible angular momentum, l, dependence of the ground state energy of normal liquid 3 He . The method of lowest order constrained variational (LOCV) which includes the three-body cluster energy and normalization constraint (LOCVE) is used with angular momentum dependent two-body correlation functions. A functional minimization is performed with respect to each l-channel correlation function. It is shown that this dependence increases the binding energy of liquid 3 He by 8% with respect to calculations without angular momentum dependent correlation functions. The l=0 state has completely different behavior with respect to other l-channels. It is also found that the main contribution from potential energy comes from the l=1 state (p-waves) and the effect of l≥11 is less than about 0.1%. The effective interactions and two-body correlations in different channels are being discussed. Finally we conclude that this l-dependence can be verified experimentally by looking into the magnetization properties of liquid helium 3 and interatomic potentials.

scholarly journals Zur Lösung des quantenmechanischen Drei-Körper-Problems

1968 ◽  
Vol 23 (4) ◽  
pp. 579-596
Author(s):  
H. Ruder
Keyword(s):  
Ground State ◽  
Physical Meaning ◽  
State Energy ◽  
Differential Operators ◽  
Perturbation Expansion ◽  
Reflection Symmetry ◽  
Body System ◽  
Rapid Convergence ◽  
Symmetry Properties ◽  
Three Body

For the description of a three-body-system 6 coordinates are introduced which take full advantage of the symmetry properties of the system. The Schrödinger equation in these coordinates is derived. Using rotational and reflection symmetry one obtains a set of l respectively l+1 coupled differential equations containing only the 3 coordinates of the triangle formed by the 3 masses. Solutions are given for special potentials and arbitrary l. The physical meaning of the differential operators appearing in the equations becomes evident from their application to the solution functions. This leads to a rearrangement of the Hamiltonian in a very transparent form and gives a hint how to get the most effective perturbation expansion. A simple example is worked out. For systems with Coulomb interaction a modification of the method is suggested by physical considerations. The calculation of the ground state energy of the Helium atom shows the rapid convergence of the procedure.

Phase diagram of cuprate high-temperature superconductors based on the optimization Monte Carlo method

2020 ◽  
Vol 34 (19n20) ◽  
pp. 2040046
Author(s):  
T. Yanagisawa ◽  
M. Miyazaki ◽  
K. Yamaji
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Wave Function ◽  
High Temperature ◽  
Hubbard Model ◽  
Ground State ◽  
State Energy ◽  
High Temperature Superconductivity ◽  
Two Dimensional ◽  
Text Model

It is important to understand the phase diagram of electronic states in the CuO2 plane to clarify the mechanism of high-temperature superconductivity. We investigate the ground state of electronic models with strong correlation by employing the optimization variational Monte Carlo method. We consider the two-dimensional Hubbard model as well as the three-band [Formula: see text]–[Formula: see text] model. We use the improved wave function that takes account of inter-site electron correlation to go beyond the Gutzwiller wave function. The ground state energy is lowered considerably, which now gives the best estimate of the ground state energy for the two-dimensional Hubbard model. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We investigate the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion [Formula: see text], the band parameter [Formula: see text] and the electron density [Formula: see text] for the Hubbard model. We show phase diagrams that include superconducting and antiferromagnetic phases. We expect that high-temperature superconductivity occurs near the boundary between antiferromagnetic phase and superconducting one. Since the three-band [Formula: see text]–[Formula: see text] model contains many-band parameters, high-temperature superconductivity may be more likely to occur in the [Formula: see text]–[Formula: see text] model than in single-band models.

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

2012 ◽  
Vol 26 (29) ◽  
pp. 1250156 ◽  
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.

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

2008 ◽  
Vol 22 (01) ◽  
pp. 33-44 ◽  
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.

scholarly journals Helium-like ions in d-dimensions: analyticity and generalized ground state Majorana solutions

2021 ◽  
Author(s):  
Adrian Mauricio Escobar ◽  
Horacio Olivares-Pilón ◽  
Norberto Aquino ◽  
Salvador Antonio Cruz-Jimenez
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Dimensional Space ◽  
Algebraic Function ◽  
Approximate Solutions ◽  
Algebraic Expression ◽  
Three Body ◽  
First Time ◽  
Analytical Expressions

Abstract Non-relativistic Helium-like ions (−e, −e, Ze) with static nucleus in a d−dimensional space (d > 1) are considered. Assuming r−1Coulomb interactions, a 2-parametric correlated Hylleraas-type trial function is used to calculate the ground state energy of the system in the domain Z ≤ 10. For odd d = 3, 5, the variational energy is given by a rational algebraic function of the variational parameters whilst for even d = 2, 4 it is shown for the first time that it corresponds to a more complicated non-algebraic expression. This twofold analyticity will hold for any d. It allows us to construct reasonably accurate approximate solutions for the ground state energy E0(Z, d) in the form of compact analytical expressions. We call them generalized Majorana solutions. They reproduce the first leading terms in the celebrated 1Z expansion, and serve as generating functions for certain correlation-dependent properties. The (first) critical charge Zc vs d and the Shannon entropy S(d)r vs Z are also calculated within the present variational approach. In the light of these results, for the physically important case d = 3 a more general 3-parametric correlated Hylleraas-type trial is used to compute the finite mass effects in the Majorana solution for a three-body Coulomb system with arbitrary charges and masses. It admits a straightforward generalization to any d as well. Concrete results for the systems e− e− e+, H+2 and H− are indicated explicitly. Our variational analytical results are in excellent agreement with the exact numerical values reported in the literature.

scholarly journals LATTICE MODEL OF ADSORPTION OF MULTISITE TRIANGLES WITH ATTRACTIVE VERTEXES: PARAMETRIZATION FOR 1, 3, 5-TRIS(PYRIDYL)BENZENE AND CU ON OXIDATED TITANIUM CARBIDE SURFACE

2020 ◽  
Vol 7 (4) ◽  
pp. 004-011
Author(s):  
O. S. Solovyeva ◽  
◽  
V. A. Gorbunov ◽  
A. V. Myshlyavtsev ◽  
◽  
...  
Keyword(s):  
Phase Diagram ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Ground State ◽  
Lattice Model ◽  
Adsorption Layer ◽  
Ground State Phase Diagram ◽  
Component System ◽  
Simple Lattice ◽  
Metal Organic

In this paper, a simple lattice model of the metal-organic adsorption layer of 1,3,5- tris(pyridyl)benzene and copper on the surface of Ti2CO2 was proposed. In this model, the selfassembly of the organometallic layer is considered as a one-component system that implicitly includes metal adatoms. The ground state phase diagram is calculated. A Monte Carlo simulation is performed using the Metropolis algorithm and the parallel temperature technique. The isotherm of the metal-organic is calculated at T = 300 K. All the results indicate the possibility of the formation of stable metal-organic phases on the Ti2CO2 surface.

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