Geometric frustration lies at the heart of many unconventional quantum phases in strongly interacting electron systems. In this talk, I will present our recent work [1], in which we analytically determine the ground state magnetization of the half-filled Hubbard model on frustrated geometries where superstable states —eigenstates that are robust against frustration —are manifest. Our results apply to a broad class of lattices, including those in which alternating magnetic and superconducting states are known to emerge. Furthermore, they provide evidence for phase transitions involving a geometric rearrangement of magnetic correlations in the thermodynamic limit. Finally, we will discuss implications for equilibrium and non-equilibrium dynamics.
[1] F. P. M. Méndez-Córdoba, J. Tindall, D. Jaksch, and F. Schlawin, arXiv:2509.07079 (2025).
