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 p oint. We argue that the transport is characterized by inelastic collis ions among thermally excited carriers at a rate of order k(B)T/(h) ove r bar. This implies that the transport at frequencies omega much less than k(B)T (h) over bar is in the hydrodynamic, collision-dominated (o r incoherent) regime, while omega much greater than k(B)T/(h) over bar is the collisionless (or phase-coherent) regime. The conductivity is argued to be e(2)/h times a nontrivial universal scaling function of ( h) over bar omega/k(B)T, and not independent of (h) over bar omega/k(B )T, as has been previously claimed or implicitly assumed. The experime ntally measured de conductivity is the hydrodynamic (h) over bar omega /k(B)T-->0 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 col lisionless (h) over bar omega/k(B)T-->infinity limit of the scaling fu nction, which actually describes phase-coherent transport with a condu ctivity given by a different universal number times e(2)/h. We provide a computation of the universal de conductivity in a disorder-free bos on model, along with explicit crossover functions, using a quantum Bol tzmann equation and an expansion in epsilon= 3 - d. The case of spin t ransport near quantum-critical points in antiferromagnets is also disc ussed. Similar ideas should apply to the transitions in quantum Hall s ystems and to metal-insulator transitions. We suggest experimental tes ts of our picture and speculate on a route to self-duality at two-dime nsional quantum-critical points.