Variational study on the ground state of the spin XY magnet

1978 ◽  
Vol 56 (7) ◽  
pp. 902-912 ◽  
Author(s):  
Masuo Suzuki ◽  
Seiji Miyashita
Keyword(s):  
Wave Function ◽  
Variational Method ◽  
Ground State ◽  
State Energy ◽  
Finite Lattice ◽  
Long Range Order ◽  
Lattice Method ◽  
Approximate Wave Function ◽  
Approximate Wave ◽  
Variational Study

An approximate wave function of the ground state of the spin [Formula: see text] XY magnet is derived using a variational method. This wave function yields estimates of the ground state energy and long-range order which agree very well with the results obtained by Betts and Oitmaa by a finite lattice method.

Electronic wave functions II. A calculation for the ground state of the beryllium atom

1950 ◽  
Vol 201 (1064) ◽  
pp. 125-137 ◽  
Keyword(s):  
Wave Function ◽  
Variational Method ◽  
Ground State ◽  
Accurate Result ◽  
Energy Criterion ◽  
Wave Functions ◽  
Exponential Functions ◽  
Approximate Wave Function ◽  
Electronic Wave Functions ◽  
Approximate Wave

An approximate wave function expressed in terms of exponential functions, spherical harmonics, etc., with numerical coefficients has been calculated for the ground state of the beryllium atom . Judged by the energy criterion this gives a more accurate result than the Hartree result which was the best previously known. This has been calculated as a trial of a fresh method of calculating atomic wave functions. A linear combination of Slater determinants is treated by the variational method. The results suggest that this will provide a more powerful and convenient method than has previously been available for atoms with more than two electrons.

scholarly journals Off-Diagonal Long-Range Order in Generalized Hubbard Models

1997 ◽  
Vol 11 (11) ◽  
pp. 1311-1335 ◽  
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.

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.

Dirac Bound States of the Killingbeck Potential Under External Magnetic Fields

2015 ◽  
Vol 70 (7) ◽  
pp. 499-505 ◽  
Author(s):  
Zahra Sharifi ◽  
Fateme Tajic ◽  
Majid Hamzavi ◽  
Sameer M. Ikhdair
Keyword(s):  
Wave Function ◽  
Magnetic Fields ◽  
Ground State ◽  
Bound States ◽  
State Energy ◽  
Potential Model ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
Ansatz Method

AbstractThe Killingbeck potential model is used to study the influence of the external magnetic and Aharanov–Bohm (AB) flux fields on the splitting of the Dirac energy levels in a 2+1 dimensions. The ground state energy eigenvalue and its corresponding two spinor components wave functions are investigated in the presence of the spin and pseudo-spin symmetric limit as well as external fields using the wave function ansatz method.

Liquid 4He: Equation of State, Compressibility and Velocity of First Sound

1998 ◽  
Vol 12 (21) ◽  
pp. 2115-2127 ◽  
Author(s):  
B. Skjetne ◽  
E. Østgaard
Keyword(s):  
Wave Function ◽  
Equation Of State ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Experimental Results ◽  
Interaction Models ◽  
First Sound ◽  
Polynomial Expression ◽  
Theoretical Results

In calculations for liquid 4 He , an investigation is made to check the accuracy of a lowest-order constrained variational (LOCV) method, using modified "healing" conditions on the two-body Jastrow wave function. Results obtained for the ground-state energy for four different interaction models are fitted by a polynomial expression, whereby the pressure, compressibility and velocity of first sound are obtained. The theoretical results are found to be in fair agreement with experimental results.

EXCITON IN ZnO FILM

2007 ◽  
Vol 21 (31) ◽  
pp. 5237-5245 ◽  
Author(s):  
HUA ZHAO ◽  
WEN XIONG ◽  
MENG-ZAO ZHU
Keyword(s):  
Wave Function ◽  
Film Thickness ◽  
Effective Mass ◽  
Ground State Energy ◽  
Ground State ◽  
Quantum Tunneling ◽  
State Energy ◽  
Zno Film ◽  
Mass Approximation ◽  
Exciton Wave Function

The present study variationally calculates the ground state energy and the first excited energy of an exciton in an ZnO film in effective mass approximation. Change of the ground state energy, the first excited energy of an exciton, and radius of the exciton with film thickness are studied, as well as the correction due to the quantum tunneling of the exciton wave function through the film.

Hypervirial theorems and perturbation theory in quantum mechanics

1965 ◽  
Vol 283 (1393) ◽  
pp. 229-237 ◽  
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Wave Functions ◽  
First Order ◽  
Optimum Energy ◽  
Arbitrary Operator ◽  
Approximate Wave Function ◽  
Hypervirial Theorem ◽  
Variational Wave Functions ◽  
Approximate Wave

Previous ideas about the way in which hypervirial theorems might be used to improve approximate wave functions are discussed. To provide a firmer foundation for these ideas, a link is established between hypervirial theorems and perturbation theory. It is proved that if the first-order perturbation correction to the expectation value of an arbitrary operator vanishes, then the approximate wave function used satisfies a certain hypervirial theorem. Conversely, if an arbitrary hypervirial theorem is satisfied by the wave function, then it is proved that the expectation values of certain operators have vanishing first-order corrections. Some consequences of the theory as applied to variational wave functions with optimum energy are developed. The results are illustrated by the use of a simple approximate wave function for the ground state of the helium atom.

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