Field-theoretical methods in quantum magnetism

  • Daniel C. Cabra
  • Pierre Pujol
Part of the Lecture Notes in Physics book series (LNP, volume 645)


We present a review of different field theory techniques that have proved very useful in the study of quantum magnets in low dimensions We first review the application of the spin-wave analysis and non-linear σ-model techniques in one and two dimensional quantum antiferromagnets. We discuss in particular the emergence of Haldane’s conjecture for spin chains and ladders within this formalism. We also present a brief discussion on the non-linear σ-model description for the two-dimensional antiferromagnet in the square lattice. In a second part we review the method of abelian bosonization and its application to the study of the XXZ spin 1/2 chain and its generalizations, such as the dimerized chain. Non-abelian bosonization is used to describe both SU (2) symmetric chains with arbitrary spin S and 2 leg ladders, rederiving Haldane’s conjecture within this formalism. The inclusion of charge degrees of freedom leading to a Hubbard or a t—J model is also discussed. Finally, we apply the abelian bosonization approach to the study of N-leg ladders in amagnetic field, which leads to a further extension of Haldane’s conjecture.


Vertex Operator Spin Chain Quantum Magnetism Topological Term Bosonic Field 
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© Springer-Verlag 2004

Authors and Affiliations

  • Daniel C. Cabra
    • 1
  • Pierre Pujol
    • 2
  1. 1.Université Louis PasteurStrasbourg
  2. 2.École Normale SupérieureLyon

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