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

Abstract

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 <{\Delta}_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 <{\Delta}_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.