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Field-theoretical methods in quantum magnetism

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

Abstract

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.

Keywords

Vertex Operator Spin Chain Quantum Magnetism Topological Term Bosonic Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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