Abstract
We describe the nature of charge transport at nonzero temperatures above the two-dimensional superfluid-insulator quantum-critical point. We argue that the transport is characterized by inelastic collisions among thermally excited carriers at a rate of order . This implies that the transport at frequencies is in the hydrodynamic, collision-dominated (or incoherent) regime, while is the collisionless (or phase-coherent) regime. The conductivity is argued to be times a nontrivial universal scaling function of , and not independent of , as has been previously claimed or implicitly assumed. The experimentally measured dc conductivity is the hydrodynamic limit of this function, and is a universal number times , even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionless limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a different universal number times . 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 . 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.
- Received 30 April 1997
DOI:https://doi.org/10.1103/PhysRevB.56.8714
©1997 American Physical Society