Chern numbers for fermionic quadrupole systems
- 21 February 1989
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 22 (4) , L111-L115
- https://doi.org/10.1088/0305-4470/22/4/001
Abstract
The authors analyse families of quantum quadrupole Hamiltonians H= Sigma alpha beta Qalpha beta Jalpha Jbeta for half-odd-integer spin, and calculate the second Chern numbers of the energy levels. Each non-zero integer occurs only a finite number of times. The adiabatic time evolution, the non-Abelian generalisation of Berry's phase, is different for each system, in contrast to Berry's example. The j=3/2 and j=1/2 cases previously analysed are the only ones with self-dual curvatures and SO(5) symmetry.Keywords
This publication has 9 references indexed in Scilit:
- Topological Invariants in Fermi Systems with Time-Reversal InvariancePhysical Review Letters, 1988
- Non-Abelian Berry’s phase, accidental degeneracy, and angular momentumJournal of Mathematical Physics, 1987
- Molecular Kramers degeneracy and non-Abelian adiabatic phase factorsPhysical Review Letters, 1987
- Appearance of Gauge Structure in Simple Dynamical SystemsPhysical Review Letters, 1984
- Quantal phase factors accompanying adiabatic changesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1984
- Holonomy, the Quantum Adiabatic Theorem, and Berry's PhasePhysical Review Letters, 1983
- Homotopy and Quantization in Condensed Matter PhysicsPhysical Review Letters, 1983
- Statistical Theory of the Energy Levels of Complex Systems. IJournal of Mathematical Physics, 1962
- On Invariant Connections over a Principal Fibre BundleNagoya Mathematical Journal, 1958