Dynamics and Transport near Quantum-critical Points

The physics of non-zero temperature dynamics and transport near quantum-critical points is discussed by a detailed study of the O(N)symmetric, relativistic, quantum field theory of a N -component scalar field in d spatial dimensions. A great deal of insight is gained from a simple, exact solution of the long-time dynamics for the N = 1 d = 1 case: this model describes the critical point of the Ising chain in a transverse field, and the dynamics in all the distinct, limiting, physical regions of its finite temperature phase diagram is obtained. The N = 3, d = 1 model describes insulating, gapped, spin chain compounds: the exact, low temperature value of the spin diffusivity is computed, and compared with NMR experiments. The N = 3, d = 2, 3 models describe Heisenberg antiferromagnets with collinear Néel correlations, and experimental realizations of quantum-critical behavior in these systems are discussed. Finally, the N = 2, d = 2 model describes the superfluid-insulator transition in lattice boson systems: the frequency and temperature dependence of the the conductivity at the quantum-critical coupling is described and implications for experiments in two-dimensional thin films and inversion layers are noted. To appear in the proceedings of the NATO Advanced Study Institute on Dynamical properties of unconventional magnetic systems, Geilo, Norway April 2-12, 1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, Dordrecht. Report number cond-mat/9705266.