Non - zero temperature transport near quantum critical points

We describe the nature of charge transport at non-zero 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 kBT/h̄. This implies that the transport at frequencies ω kBT/h̄ is in the hydrodynamic, collision-dominated (or ‘incoherent’) regime, while ω kBT/h̄ is the collisionless (or ‘phasecoherent’) regime. The conductivity is argued to be e/h times a non-trivial universal scaling function of h̄ω/kBT , and not independent of h̄ω/kBT , as has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamic h̄ω/kBT → 0 limit of this function, and is a universal number times e2/h, even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionless h̄ω/kBT →∞ limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a different universal number times e2/h. We provide the first computation of the universal d.c. 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 new route to self-duality at two-dimensional quantum critical points. Typeset using REVTEX