Nonzero-temperature transport near quantum critical points

We describe the nature of charge transport at nonzero temperatures (T) above the two-dimensional (d) superfluid-insulator quantum-critical point. We argue that the transport is characterized by inelastic collisions among thermally excited carriers at a rate of order k₁T/. This implies that the transport at frequencies k₁T/ is in the hydrodynamic, collision-dominated (or incoherent) regime, while k₁T/ is the collisionless (or phase-coherent) regime. The conductivity is argued to be e^2/h times a nontrivial universal scaling function of /k₁T, and not independent of /k₁T, as has been previously claimed or implicitly assumed. The experimentally measured dc conductivity is the hydrodynamic /k₁T0 limit of this function, and is a universal number times e^2/h, even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionless /k₁T limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a different universal number times e^2/h. We provide a computation of the universal dc conductivity in a disorder-free boson model, along with explicit crossover functions, using a quantum Boltzmann equation and an expansion in =3-d. The case of spin transport near quantum-critical points in antiferromagnets is also discussed. Similar ideas should apply to the transitions in quantum Hall systems and to metal-insulator transitions. We suggest experimental tests of our picture and speculate on a route to self-duality at two-dimensional quantum-critical points.