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
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Kluwer Academic Publishers
About this chapter
Cite this chapter
Fisher, M.P.A. (2004). Duality in low dimensional quantum field theories. In: Baeriswyl, D., Degiorgi, L. (eds) Strong interactions in low dimensions. Physics and Chemistry of Materials with Low-Dimens, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3463-3_13
Download citation
DOI: https://doi.org/10.1007/978-1-4020-3463-3_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-1798-8
Online ISBN: 978-1-4020-3463-3
eBook Packages: Springer Book Archive