Fractional Quantum Geometry in Topological Mott Regime

Abstract: Inspired by recent interests in quantum geometry in electronic bands, we consider a two-dimensional topological Mott insulator, i.e. chiral spin liquid, whose spinon bands develop nontrivial band topological and quantum geometry. The virtual polarization of the gapped charge sector transfers the electromagnetic drive to the charge-neutral spinons through the emergent U(1) gauge field, producing a tensor Ioffe-Larkin response and enabling two complementary optical protocols for measurements. In the off-shell (low-frequency) regime, a self-calibrated ratio of the physical longitudinal and Hall conductivities yields the spinon Chern number without the microscopic knowledge of the charge response. In the on-shell (resonant) regime, combining the inverse Ioffe-Larkin response with the Kramers-Kronig relation enables reconstruction of the quantum-metric and Berry-curvature spectral densities. Our approach directly applies to the triangular lattice Hofstadter-Hubbard model in Moiré systems, can be well adapted to other triangular lattice antiferromagnets such as Nb$_3$Br$_8$ with appropriate modifications. We establish a unified framework for quantitatively probing the quantum geometry of fractionalized quasiparticles in topological Mott regime.