Universal transport near a quantum critical Mott transition in two dimensions

We discuss the universal-transport signatures near a zero-temperature continuous Mott transition between a Fermi liquid and a quantum spin liquid in two spatial dimensions. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the spin liquid, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We present a controlled calculation of the value of the zero-temperature universal resistivity jump predicted to occur at the transition. More generally, the behavior of the universal scaling function that collapses the temperature- and pressure-dependent resistivity is derived, and is shown to bear a strong imprint of the emergent gauge fluctuations. We further predict a universal jump of the thermal conductivity across the Mott transition, which derives from the breaking of conformal invariance by the damped gauge field, and leads to a violation of the Wiedemann-Franz law in the quantum critical region. A connection to the quasitriangular organic salts is made, where such a transition might occur. Finally, we present some transport results for the pure rotor $O(N)$ conformal field theory.