Strong-coupling expansion and effective hamiltonians
arXiv:1005.2495 · doi:10.1007/978-3-642-10589-0_20
Abstract
When looking for analytical approaches to treat frustrated quantum magnets, it is often very useful to start from a limit where the ground state is highly degenerate. This chapter discusses several ways of deriving {effective Hamiltonians} around such limits, starting from standard {degenerate perturbation theory} and proceeding to modern approaches more appropriate for the derivation of high-order effective Hamiltonians, such as the perturbative continuous unitary transformations or contractor renormalization. In the course of this exposition, a number of examples taken from the recent literature are discussed, including frustrated ladders and other dimer-based Heisenberg models in a field, as well as the mapping between frustrated Ising models in a transverse field and quantum dimer models.
To appear as a chapter in "Highly Frustrated Magnetism", Eds. C. Lacroix, P. Mendels, F. Mila
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