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

Abstract: We investigate the emergence of altermagnetism -- a collinear magnetic phase characterized by large non-relativistic spin splitting and zero net magnetization -- driven by electronic correlations on 3x3 geometrically frustrated square lattice. Using exact diagonalization of the simple and the extended Hubbard model, we analyze the interplay between on-site repulsion U , nearest-neighbor (NN) Coulomb interaction V and geometric frustration across various filling factors (N=8,9,10). Unlike traditional models that rely on single-particle anisotropy or specific sublattice geometries, our results demonstrate that altermagnetic signatures arise from many-body fluctuations in doped Mott insulators. We find that while geometric frustration suppresses altermagnetism at half-filling (N=9), carrier doping (hole (N=8) or electron (N=10)) stabilizes robust, rotationally symmetric altermagnetic correlations. Furthermore, we identify a critical threshold for the NN interaction V at intermediate coupling (U=4) where the altermagnetic state in the electron-doped sector undergoes a first-order-like transition, whereas strong coupling (U=10) stabilizes well-formed local moments and preserves the anisotropic spin texture. This work establishes a fluctuation-mediated route to altermagnetism on symmetric geometrically frustrated lattices and identify carrier concentration and the NN Coulomb interaction as a critical tunable parameter for controlling magnetic anisotropy in strongly correlated systems.