Spin-charge separation in two dimensions: spinon-chargon gauge theories from duality

Strong interactions between electrons in two dimensions can realize phases where their spins and charges separate. We capture this phenomenon within a dual formulation. Focusing on square lattices, we analyze the long-wavelength structure of vortices when the microscopic particles -- electrons or spinful bosons -- are near half-filling. These conditions lead to a compact gauge theory of spinons and chargons, which arise as the fundamental topological defects of the low-energy vortices. The gauge theory formulation is particularly suitable for studying numerous exotic phases and transitions. We support the general analysis by an exact implementation of the duality of a coupled-wire array. Finally, we demonstrate how the latter can be exploited to construct parent Hamiltonians for fractional phases and their transitions