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From Möbius aromaticity to gapped spin liquids

Motivated by the concept of Möbius aromatics in organic chemistry, I will discuss the tight-binding Hubbard model on ring-shaped molecules with and without a half-quantum of magnetic flux running through their center. Depending on the strength of hopping and interaction, the ground state can be a so-called fragile Mott insulator (FMI) that is distinct from a conventional insulator through its nontrivial transformation properties under point group symmetry operations. Including next-nearest-neighbor hoppings gives rise to FMI states that belong to multidimensional irreducible representations of the molecular point group. Going beyond the individual molecule, I will further discuss the many-body ground state of a two-dimensional lattice of FMI molecules that are weakly coupled. The problem maps to frustrated spin systems with broken SU(2) symmetry. On the triangular lattice the ground state develops Neel order, which corresponds to a charge-ordered state of the molecules. More interestingly, on the honeycomb lattice we find a nondegenerate gapped spin liquid ground state that preserves all symmetries, but transforms nontrivially under point group operations. Our microscopic model therefore realizes an intrinsically interacting fermionic symmetry protected topological (SPT) phase.