EFFECT OF DIMENSIONALITY ON THE GROUND STATE PROPERTIES OF THE EXTENDED HUBBARD MODEL USING THE HIGHLY SIMPLIFIED CORRELATED VARIATIONAL APPROACH
DOI:
https://doi.org/10.60787/jnamp.vol73no.741Keywords:
Extended Hubbard model, highly simplified correlated variational approach, dimensionality effect, singlet-triplet energy gapAbstract
The extended Hubbard model (EHM) captures essential interactions (U, V, J) in strongly correlated electron systems, yet unified variational studies of spatial dimensionality effects remain sparse. Using the Highly Simplified Correlated Variational Approach (HSCVA), we investigate 24-site setups in 1D, 2D and 3D lattice with preserved coordination numbers z = 2, 4, 6. We compute the singlettriplet energy gap ( ) and critical exchange coupling (Jc) across U and V. The V = 0 singlet-triplet transition is universal across dimensions. For repulsive V/2t, the gap becomes negative ( ), signaling triplet ground-state stability with saturation values scaling by coordination number: -4.20 (1D), -8.00 (2D) and -15.99 (3D). Critical coupling Jc exhibits linear antisymmetric scaling in 1D and 2D, while 3D systems show non-linear growth for U > 0. These results provide quantitative benchmarks for dimensional crossovers in correlated systems.
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