Quantum geometry tuned magnetic exchange in a Mott insulator

Quantum geometry has recently emerged as an important guiding principle for understanding and engineering properties of quantum materials. While it is well known that a nonzero quantum metric bounds the spread of Wannier orbitals from below, the consequences of this absence of localization are less explored for strongly interacting Mott insulators, whose theory is formulated in terms of exponentially localized Wannier functions. It would therefore be valuable to reconcile these two divergent pictures, and understand how quantum geometry in general affects the competition between correlated phases. In this work, we propose that quantum geometry intrinsic to Bloch wavefunctions can act as a tuning knob for effective magnetic interactions in the presence of strong interactions. We illustrate this proposal by formulating a three-band model with independently tunable dispersion, band gaps, and quantum geometry. Using fermion-sign-free determinant quantum Monte Carlo (DQMC) simulations, we study the half-filled center band and reveal a competition between ferromagnetism and antiferromagnetism as a function of Wannier function spread, thereby interpolating between the two intuitive pictures of flavor polarization and simple Mott antiferromagnetism.