Abstract
Problems of strongly interacting electrons can be greatly simplified by reducing them to effective quantum spin models. The initial step is renormalization of the Hamiltonian into a lower energy subspace. The positive and negative U Hubbard models are explicitly transformed into the Heisenberg and −x − xz models respectively. Basic tools of quantum magnetism are introduced and used: spin coherent states path integral, spin wave theory, and continuum theory of rotators. The last lecture concerns pseudospin approaches to superconductivity and superfluidity. The SO(3) rotator theory for the −x − xz model describes the charge density wave to superconductor transition for e.g. doped bismuthates. Analogously, Zhang’s theory for collective modes of high Tc cuprates describes the antiferromagnet to d-wave superconductor transition using SO(5) rotators. Finally, the Magnus force on two dimensional vortices and their momentum, are derived from the Berry phase of the spin path integral.
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Auerbach, A., Berruto, F., Capriotti, L. (2000). Quantum Magnetism Approaches to Strongly Correlated Electrons. In: Morandi, G., Sodano, P., Tagliacozzo, A., Tognetti, V. (eds) Field Theories for Low-Dimensional Condensed Matter Systems. Springer Series in Solid-State Sciences, vol 131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04273-1_5
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DOI: https://doi.org/10.1007/978-3-662-04273-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08650-2
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