Flux Hamiltonians, Lie Algebras and Root Lattices With Minuscule Decorations

Details Flux Hamiltonians, Lie Algebras and Root Lattices With Minuscule Decorations Flux Hamiltonians, Lie Algebras and Root Lattices With Minuscule Decorations

2008-02-23

arxiv.org/abs/0802.3466v1

Ann. Phys., vol. 324, Issue 2 (2009), 267-95

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

10.1016/j.aop.2008.06.005

We study a family of Hamiltonians of fermions hopping on a set of lattices in the presence of a background gauge field. The lattices are constructed by decorating the root lattices of various Lie algebras with their minuscule representations. The Hamiltonians are, in momentum space, themselves elements of the Lie algebras in these same representations. We describe various interesting aspects of the spectra--which exhibit a family resemblance to the Dirac spectrum, and in many cases are able to relate them to known facts about the relevant Lie algebras. Interestingly, various realizable lattices such as the kagom\'{e} and pyrochlore can be given this Lie algebraic interpretation and the particular flux Hamiltonians arise as mean-field Hamiltonians for spin-1/2 Heisenberg models on these lattices.

Affiliated with

Also associated with

No associations

Rating

Flux Hamiltonians, Lie Algebras and Root Lattices With Minuscule Decorations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Flux Hamiltonians, Lie Algebras and Root Lattices With Minuscule Decorations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Flux Hamiltonians, Lie Algebras and Root Lattices With Minuscule Decorations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-427002