Two-dimensional quantum Heisenberg antiferromagnet at low temperatures

Sudip Chakravarty, Bertrand I. Halperin, and David R. Nelson
Phys. Rev. B 39, 2344 – Published 1 February 1989
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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 σ 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 σ model are analyzed approximately using the one-loop renormalization-group method. When the model has long-range order at T=0, 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 σ 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 T. 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 La2CuO4, if the spin-wave velocity is assumed to be 0.67 eV Å. We also argue that the data on La2CuO4 cannot be easily explained by any model in which an isolated CuO2 layer would not have long-range antiferromagnetic order at T=0. Our theory also predicts a quasielastic peak of a few meV width at 300 K when kξ1 (where k is wave-vector transfer and ξ 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

Authors & Affiliations

Sudip Chakravarty*

  • Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794

Bertrand I. Halperin and David R. Nelson

  • Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138

  • *Permanent address: Department of Physics, University of California at Los Angeles, Los Angeles, CA 90024.

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Vol. 39, Iss. 4 — 1 February 1989

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