Dynamics and transport near quantum-critical points

TL;DR

This paper investigates the dynamics and transport phenomena near quantum-critical points across various models and dimensions, providing exact solutions and experimental comparisons for different physical systems.

Contribution

It offers exact solutions for the dynamics of quantum-critical models in one dimension and explores transport properties in higher dimensions, connecting theory with experiments.

Findings

Exact dynamics for N=1, d=1 model related to Ising chain critical point

Computed low-temperature spin diffusivity in N=3, d=1 model and compared with NMR data

Described conductivity behavior at quantum-critical coupling in N=2, d=2 model

Abstract

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 N\'{e}el 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.