scholarly journals On the Validity of the Dynamical Mean-Field Approximation for Studying the Two-Dimensional Hubbard Model on a Square Lattice

2010 ◽  
Vol 2010 ◽  
pp. 1-5 ◽  
Author(s):  
A. N. Ribeiro ◽  
C. A. Macedo
Keyword(s):  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Mean Field ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Two Dimensional ◽  
Infinite Dimensions ◽  
Antiferromagnetic Correlations ◽  
Half Filling

The dynamical mean-field approximation (DMFA) becomes exact in the limit of infinite dimensions, and allows results to be obtained in a nonperturbative regime without the limitations normally found with exact diagonalization (ED) and quantum Monte Carlo (QMC) methods. In this paper, we investigate the applicability of the method to lattices with small coordination number in special situations. Specifically we use this approximation to study the two-dimensional (2D) Hubbard model on a square lattice far from half filling. In this situation, we calculate the specific heat and find that when the filling decreases, that is, antiferromagnetic correlations become less important, the agreement between DMFA and QMC results increases. Our results show that the DMFA can be a valuable technique for studying the thermodynamic properties of the Hubbard model also on a square lattice, but within a parameter range in which the antiferromagnetic correlations are not important.

scholarly journals Collective in-plane magnetization in a two-dimensional XY macrospin system within the framework of generalized Ott–Antonsen theory

2020 ◽  
Vol 378 (2171) ◽  
pp. 20190259 ◽  
Author(s):  
Irina V. Tyulkina ◽  
Denis S. Goldobin ◽  
Lyudmila S. Klimenko ◽  
Igor S. Poperechny ◽  
Yuriy L. Raikher
Keyword(s):  
Magnetic Moments ◽  
Mean Field ◽  
Ferromagnetic State ◽  
Dipole Interaction ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Two Dimensional ◽  
Stripe Structure ◽  
First Order Phase

The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in two-dimensional XY arrays is addressed. The system is modelled as a plane structure of identical single-domain particles arranged in a square lattice and coupled by the magnetic dipole–dipole interaction; all the particles possess a strong easy-plane magnetic anisotropy. The basic state of the system in the considered temperature range is an antiferromagnetic (AF) stripe structure, where the macrospins (particle magnetic moments) are still involved in thermofluctuational motion: the superparamagnetic blocking T b temperature is lower than that ( T af ) of the AF transition. The description is based on the stochastic equations governing the dynamics of individual magnetic moments, where the interparticle interaction is added in the mean-field approximation. With the technique of a generalized Ott–Antonsen theory, the dynamics equations for the order parameters (including the macroscopic magnetization and the AF order parameter) and the partition function of the system are rigorously obtained and analysed. We show that inside the temperature interval of existence of the AF phase, a static external field tilted to the plane of the array is able to induce first-order phase transitions from AF to ferromagnetic state; the phase diagrams displaying stable and metastable regions of the system are presented. This article is part of the theme issue ‘Patterns in soft and biological matters’.

ANALYSIS OF THE TWO-DIMENSIONAL NEGATIVE-U HUBBARD MODEL BY COMPOSITE OPERATOR METHOD

1996 ◽  
Vol 10 (22) ◽  
pp. 2745-2756 ◽  
Author(s):  
T. DI MATTEO ◽  
F. MANCINI ◽  
S. MARRA ◽  
H. MATSUMOTO
Keyword(s):  
Hubbard Model ◽  
Chemical Potential ◽  
Particle Density ◽  
Mean Field ◽  
Finite Size ◽  
Operator Method ◽  
Field Approximation ◽  
Composite Operator ◽  
Mean Field Approximation ◽  
Two Dimensional

The two-dimensional negative-U Hubbard model is studied by means of the composite operator approach. In a generalized mean-field approximation we calculate different quantities, as the chemical potential, the double occupancy, the static uniform spin magnetic susceptibility and the density of states for various values of the particle density, attractive on-site interaction and temperature. Comparison with the results obtained by numerical analysis on finite size lattices shows a good agreement.

PHASE DIAGRAM OF STRIPE ORDER IN THE EXTENDED HUBBARD MODEL

2000 ◽  
Vol 14 (29n31) ◽  
pp. 3508-3513 ◽  
Author(s):  
MASARU KATO
Keyword(s):  
Hubbard Model ◽  
Coulomb Interaction ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Extended Hubbard Model ◽  
Stable States ◽  
Stripe Order

The extended Hubbard model with the nearest-neighbor Coulomb interaction on the square lattice is studied within the mean-field approximation. The stable states for 8×8 sites lattice with the periodic boundary condition and the electron filling n=0.875, as well as for 10×10 lattice and n=0.80, are obtained. For 8×8 lattice where quarter-filled straight stripe is expected because of the long-range Coulomb interaction, the cross stripe phases become stable.

DISCUSSION ON THE MEAN FIELD APPROXIMATION IN THE RVB THEORY

1988 ◽  
Vol 02 (10) ◽  
pp. 1205-1209 ◽  
Author(s):  
R.B. TAO ◽  
X. HU ◽  
M. SUZUKI
Keyword(s):  
Hubbard Model ◽  
Strong Correlation ◽  
Magnetic System ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Hubbard Hamiltonian ◽  
Half Filling ◽  
The Mean

Baskaran’s mean field approximation of the Hubbard Hamiltonian with strong correlation and half-filling is discussed. Our calculations show that his decoupling of the Hamiltonian is not permissible in the half-filling case and that it destroys the equivalence of the Hubbard model to the Heisenberg magnetic system and violates some spin-spin relations.

scholarly journals Энергетический спектр и оптические свойства фуллерена C-=SUB=-80-=/SUB=-(I-=SUB=-h-=/SUB=-) в модели Хаббарда

2021 ◽  
Vol 129 (10) ◽  
pp. 1227
Author(s):  
А.В. Силантьев
Keyword(s):  
Group Theory ◽  
Hubbard Model ◽  
Symmetry Group ◽  
Mean Field ◽  
Analytical Form ◽  
Field Approximation ◽  
Energy Spectra ◽  
Mean Field Approximation ◽  
The Mean

The anticommutative Green’s functions were derived in an analytical form, and the energy spectra of С80 fullerene and endohedral Y3N@C80 fullerene of symmetry group Ih were obtained within the Hubbard model in the mean-field approximation. Using group theory methods, the classification of energy states was carried out, and the allowed transitions in the energy spectra of С80 and Y3N@C80 molecules of symmetry group Ih were determined.

POSSIBLE COEXISTENCE OF ANTIFERROMAGNETISM AND SUPERCONDUCTIVITY IN THE HUBBARD MODEL

1988 ◽  
Vol 01 (09n10) ◽  
pp. 341-347 ◽  
Author(s):  
SHEN JUE-LIAN ◽  
SU ZHAO-BIN ◽  
DONG JIN-MING ◽  
YU LU
Keyword(s):  
Hubbard Model ◽  
High Temperature Superconductivity ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Antiferromagnetic Order ◽  
Effective Hamiltonian ◽  
Hamiltonian Approach ◽  
Theoretical Approaches ◽  
The Mean

The Hubbard model in the nearly half-filled case was studied in the mean field approximation using the effective Hamiltonian approach. Both antiferromagnetic order parameter and condensation of singlet pairs were considered. In certain parameter range the coexistence of antiferromagnetism and superconductivity is energetically favorable. Relations to the high temperature superconductivity and other theoretical approaches are also discussed.

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