Abstract
It is argued that the long-wavelength, low-temperature behavior of a two-dimensional quantum Heisenberg antiferromagnet can be described by a quantum nonlinear model in two space plus one time dimension, at least in the range of parameters where the model has long-range order at zero temperature. The properties of the quantum nonlinear model are analyzed approximately using the one-loop renormalization-group method. When the model has long-range order at , the long-wavelength behavior at finite temperatures can be described by a purely classical model, with parameters renormalized by the quantum fluctuations. The low-temperature behavior of the correlation length and the static and dynamic staggered-spin-correlation functions for the quantum antiferromagnet can be predicted, in principle, with no adjustable parameters, from the results of simulations of the classical model on a lattice, combined with a two-loop renormalization-group analysis of the classical nonlinear model, a calculation of the zero-temperature spin-wave stiffness constant and uniform susceptibility of the quantum antiferromagnet, and a one-loop analysis of the conversion from a lattice cutoff to the wave-vector cutoff introduced by quantum mechanics when the spin-wave frequency exceeds . Applying this approach to the spin-½ Heisenberg model on a square lattice, with nearest-neighbor interactions only, we obtain a result for the correlation length which is in good agreement with the data of Endoh et al. on Cu, if the spin-wave velocity is assumed to be 0.67 eV . We also argue that the data on Cu cannot be easily explained by any model in which an isolated Cu layer would not have long-range antiferromagnetic order at . Our theory also predicts a quasielastic peak of a few meV width at 300 K when (where is wave-vector transfer and is the correlation length). The extent to which this dynamical prediction agrees with experiments remains to be seen. In an appendix, we discuss the effect of introducing a frustrating second-nearest-neighbor coupling for the antiferromagnet on the square lattice.
- Received 18 August 1988
DOI:https://doi.org/10.1103/PhysRevB.39.2344
©1989 American Physical Society