High Temperature Relaxational Dynamics in Low-dimensional Quantum Field Theories

This paper presents a unified perspective on the results of two recent works (C. Buragohain and S. Sachdev cond-mat/9811083 and S. Sachdev condmat/9810399) along with additional background. We describe the low frequency, non-zero temperature, order parameter relaxational dynamics of a number of systems in the vicinity of a quantum critical point. The dynamical correlations are properties of the high temperature limit of renormalizable quantum field theories in spatial dimensions d = 1, 2. We study, as a function of d and the number of order parameter components, n, the crossover from the finite frequency, “amplitude fluctuation”, gapped quasiparticle mode in the quantum paramagnet (or Mott insulator), to the zero frequency “phase” (n ≥ 2) or “domain wall” (n = 1) relaxation mode near the ordered phase. Implications for dynamic measurements on the high temperature superconductors and antiferromagnetic spin chains are noted.