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

Abstract

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.