Critical theory of quantum spin chains

Phys. Rev. B 36, 5291 – Published 1 October 1987
Ian Affleck and F. D. M. Haldane


The relation between quantum spin chains and conformal field theories is reexamined. Using a generalized Hubbard model representation it is argued that the critical theory for generic half-odd-integer spin antiferromagnets is the Wess-Zumino-Witten model (WZW model) with topological coupling, k=1, whereas generic integer spin antiferromagnets have an energy gap. The higher-k WZW models (which describe integrable higher spin models) are multicritical points in the space of all spin Hamiltonians. The k=1 WZW model represents a stable fixed point for many theories including WZW models of arbitrary odd k with relevant operators added, generalized Hubbard or Thirring models with an odd number of colors and the O(3) σ model at topological angle θ=π.


  • Received 30 March 1987
  • Published in the issue dated 1 October 1987

© 1987 The American Physical Society

Authors & Affiliations

Ian Affleck

  • Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544

F. D. M. Haldane

  • Physics Department, University of California at San Diego, La Jolla, California 92093

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