Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices

We study the half-filled Hubbard model on a one-parameter family of vortex-full square lattices ranging from the isotropic case to weakly coupled Hubbard dimers. The ground-state phase diagram consists of four phases: A semi-metal and a band insulator which are connected to the weak-coupling limit, and a magnetically ordered N\'eel phase and a valence bond crystal (VBC) which are linked to the strong-coupling Mott limit. The phase diagram is obained by quantum Monte Carlo (QMC) and continuous unitary transformations (CUTs). The CUT is performed in a two-step process: Non-perturbative graph-based CUTs are used in the Mott insulating phase to integrate out charge fluctuations. The resulting effective spin model is tackled by perturbative CUTs about the isolated dimer limit yielding the breakdown of the VBC by triplon condensation. We find three scenarios when varying the interaction for a fixed anisotropy of hopping amplitudes: i) one direct phase transition from N\'eel to semi-metal, ii) two phase transitions VBC to N\'eel and N\'eel to semi-metal, or iii) a smooth crossover from VBC to the band insultor. Our results are consistent with the absence of spin-liquid phases in the whole phase diagram.