M\"obius molecules and fragile Mott insulators

TL;DR

This paper explores the concept of fragile Mott insulators in ring-shaped molecules with Hubbard interactions and magnetic flux, revealing a duality based on molecule size and flux presence, and discovering new FMI states with complex symmetries.

Contribution

It extends the concept of fragile Mott insulators to specific molecular systems and uncovers a duality related to molecule size and magnetic flux effects.

Findings

Duality between $4n$ and $4n+2$ site molecules regarding FMI and band insulator states.

Introduction of next-nearest-neighbor hopping leads to new FMI states with complex symmetries.

Rich phase diagram with flux-dependent transitions between insulating states.

Abstract

Motivated by the concept of M\"obius 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, a 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.