arXiv subjects

Md Fahad Equbal

Publications and source records attributed to Md Fahad Equbal.

5 recordsLinked to original sources

arXiv2026

Finite-size effects and interaction-driven crossovers in quarter-filled attractive Hubbard model: Exact diagonalization, DMRG and machine-learning analysis

We investigate the quarter-filled attractive Hubbard model on finite-width cylindrical lattices using exact diagonalization (ED), density-matrix renormalization group (DMRG) and unsupervised machine-learning-based techniques. Analysis of the ground-state energetics, local observables and correlation functions reveals a continuous interaction-driven crossover from weakly correlated fermions to a regime dominated by tightly bound singlet pairs. This crossover originates from the competition between kinetic-energy-driven fermionic itinerancy and interaction-driven onsite pair formation and exhibits behavior consistent with the BCS--BEC crossover in the thermodynamic limit. Hole-binding-energy calculations provide direct energetic evidence for pair formation: the two-hole binding energy remains negative throughout the attractive regime whereas three-hole binding emerges only at sufficiently strong attraction and exhibits pronounced finite-size dependence. To obtain an unbiased characterization of the correlation landscape, we apply principal component analysis (PCA) and uniform manifold approximation and projection (UMAP) to the real-space correlation matrices. PCA reveals a systematic redistribution of correlation variance whereas UMAP identifies a clear separation between weak- and strong-pairing regimes. Both machine-learning-based approaches independently identify the same crossover region inferred from conventional observables while providing an order-parameter-independent characterization of the underlying reorganization of many-body correlations. Finite-size scaling analyses of the pairing structure factor and the leading PCA variance ratio demonstrate that these signatures remain robust with increasing system size.

cond-mat.str-el↗

arXiv2026

Emergence of correlation-driven altermagnetism in Hubbard model on geometrically frustrated lattice-clusters

We investigate the emergence of correlation-driven altermagnetism in simple and extended Hubbard model on geometrically frustrated lattice-clusters using exact diagonalization. By systematically tuning the degree of geometric frustration across different cluster geometries -- including the fully frustrated 3x3 torus, the partially frustrated 2x3 cylinder and the unfrustrated 2x4 cylindrical lattice -- we isolate the necessary conditions for compensated anisotropic spin order. At half-filling on 3x3 lattice, the average altermagnetic spin-response <Δ_spin> remains small despite robust local moment formation, indicating that localized moments alone are insufficient to break directional symmetry. In contrast, the introduction of a single mobile charge carrier (hole or electron) induces a finite <Δ_spin> that increases monotonically with on-site interaction U . This altermagnetic phase is characterized by a d-wave-like alternating sign structure in real-space correlations, a broad momentum-space distribution in the altermagnetic structure factor S_alm(q) and a distinct particle-hole asymmetry with significantly enhanced response for one-electron-doped system. We demonstrate that these correlations remain zero on the unfrustrated 2x4 lattice, establishing geometric frustration as a fundamental prerequisite. The inclusion of nearest-neighbor Coulomb repulsion V weakens the altermagnetic correlations in 3x3 lattice through enhanced electronic localization but facilitates the onset of altermagnetic order in 2x3 lattice beyond a critical threshold. Finally, we show that the anisotropy parameter A is non-zero only for degenerate ground states, revealing that macroscopic symmetry breaking on finite clusters requires a confluence of geometric frustration and ground-state degeneracy.

cond-mat.str-el↗

arXiv2026

Principal Component Analysis of Competing Correlations in Quarter-Filled Hubbard Models

We present an unsupervised learning analysis of correlation hierarchies in the quarter-filled simple and extended Hubbard models by applying principal component analysis (PCA) to exact-diagonalization (ED) data on 3x4 and 4x4 cylindrical clusters. While the non-interacting limit (U=0) provides a finite-size reference, increasing on-site repulsion U induces localization and reorganizes the low-energy spectrum. For the extended model, we examine moderate (U=4) and strong (U=10) coupling regimes, where conventional structure factors reveal familiar crossovers among charge, spin and local-pairing correlations. PCA of the corresponding correlation matrices captures these crossovers directly from the data, without assuming predefined order parameters by identifying charge-dominated, spin-dominated and pairing-dominated regimes through variance condensation into leading components. This establishes PCA as a transparent, model-agnostic framework for uncovering the hierarchy and competition of correlation channels in finite Hubbard clusters, providing a bridge between exact diagonalization and modern machine-learning diagnostics in strongly correlated systems.

cond-mat.str-el↗

arXiv2026

Spin-resolved Mott crossover and entanglement in the half-filled Hubbard model

We investigate the interaction-driven reorganization of spin and charge correlations in finite Hubbard clusters using exact diagonalization. Focusing on half-filled and lightly doped square lattices, we analyze spin-resolved charge-gaps, local observables, two-point correlation functions, entanglement measures, principal component analysis (PCA) of correlation matrices and quantum-geometry-based distance metrics. At half-filling, we observe the emergence of a robust Mott gap whose spin-dependent component is controlled by the effective exchange energy scale J~4t^2/U at strong coupling, confirming that residual spin dynamics govern the separation between the lowest-spin and the next higher-spin charge excitation channels. Distinct cluster geometries and boundary conditions reveal how spin-singlet versus finite-spin ground-state influence charge and spin responses. Upon one-hole doping, the spin-resolved charge-gaps collapses, indicating restored compressibility and metallic behavior. PCA and quantum-geometry-based analysis provide complementary data-driven and wavefunction-based perspectives on correlation-driven Mott crossover phenomena. Our results demonstrate that finite-size Hubbard clusters exhibit clear signatures of the Mott physics, spin-charge interplay and emergent exchange energy scales, offering a unified microscopic picture of interaction-induced electronic reorganization.

cond-mat.str-el↗

arXiv2025

Binding of holes and competing spin-charge order in simple and extended Hubbard model on cylindrical lattice: An exact diagonalization study

We investigate the binding of holes and the emergence of competing spin-charge order in the simple and extended Hubbard model using exact diagonalization on the 3x4 cylindrical lattice. For the simple Hubbard model (V=0), we find weakly bound hole pairing mediated by magnetic correlations at intermediate repulsive U, without any evidence of phase separation. Introducing nearest-neighbor interaction V reveals a rich phase diagram: attractive V drives multi-hole clustering and phase separation with localized magnetic quenching, while repulsive V stabilizes charge-density-wave (CDW) order that coexists with bound hole pairs within a modulated magnetic background. At strong coupling (U=10), the competition sharpens, with attractive V overcoming on-site repulsion to form magnetically quenched clusters and repulsive V producing robust CDW order that constrains pairing. Real-space analysis of spin and charge correlations provides microscopic evidence of distinct binding mechanisms -- phase separation versus correlation-mediated pairing -- depending on the sign and strength of intersite interaction V . Our results establish a comprehensive picture of how nonlocal Coulomb interactions reshape the landscape of hole-binding and collective order in correlated electron systems.

cond-mat.str-el↗