Duality in low dimensional quantum field theories

  • Matthew P. A. Fisher
Part of the Physics and Chemistry of Materials with Low-Dimens book series (PCMALS, volume 25)

In some strongly correlated electronic materials Landau’s quasiparticle concept appears to break down, suggesting the possibility of new quantum ground states which support particle-like excitations carrying fractional quantum numbers. Theoretical descriptions of such exotic ground states can be greatly aided by the use of duality transformations which exchange the electronic operators for new quantum fields. This chapter gives a brief and self-contained introduction to duality transformations in the simplest possible context - lattice quantum field theories in one and two spatial dimensions with a global Ising or XY symmetry. The duality transformations are expressed as exact operator change of variables performed on simple lattice Hamiltonians. A Hamiltonian version of the Z2 gauge theory approach to electron fractionalization is also reviewed. Several experimental systems of current interest for which the ideas of duality might be beneficial are briefly discussed.

Keywords: Duality, quantum Ising model, quantum XY model, rotors, Z2 gauge theory, fractionalization


Gauge Theory Domain Wall Ising Model Quantum Phase Transition Duality Transformation 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Matthew P. A. Fisher
    • 1
  1. 1.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraUSA

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