Möbius molecules and fragile Mott insulators

Motivated by the concept of Möbius aromatics in organic chemistry, we extend the recently introduced concept of fragile Mott insulators (FMI) to ring-shaped molecules with repulsive Hubbard interactions threaded by a half-quantum of magnetic flux (hc/2e). In this context, an FMI is the insulating ground state of a finite-size molecule that cannot be adiabatically connected to a single Slater determinant, i.e., to a band insulator, provided that time-reversal and lattice translation symmetries are preserved. Based on exact numerical diagonalization for finite Hubbard interaction strength U and existing Bethe-ansatz studies of the one-dimensional Hubbard model in the large-U limit, we establish a duality between Hubbard molecules with 4n and 4n+2 sites, with n integer. A molecule with 4n sites is an FMI in the absence of flux but becomes a band insulator in the presence of a half-quantum of flux, while a molecule with 4n+2 sites is a band insulator in the absence of flux but becomes an FMI in the presence of a half-quantum of flux. Including next-nearest-neighbor hoppings gives rise to new FMI states that belong to multidimensional irreducible representations of the molecular point group, giving rise to a rich phase diagram.