Friday, February 5, 2010

Desperately seeking spin liquids III

It was wonderful having Bruce Normand visit UQ this week. It is great having a visitor come who meets individually with students, postdocs, and faculty and discusses their work at length. I think we all learnt a lot and appreciated the constructive feedback.

Bruce made me aware of a nice accessible review Frontiers in frustrated magnetism that he just published in Contemporary Physics.
The focus is on spin liquids: whether they exist in real materials and/or Heisenberg lattice models. This gives more background relevant to a conjecture I discussed in two previous posts. From Bruce's seminar and discussions I now realise there is a strong candidate counter-example to the conjecture. That is the Heisenberg model on the isotropic triangular lattice with multiple spin exchange. The best numerical evidence of a spin liquid (unbroken lattice symmetry, spin gap) is in this paper. It would be great if more numerical work was done on this model using new methods such as those based on tensor-network states.


  1. At the end of Bruce's talk, I felt that I understood the spin-liquid concept more than I ever had before.

    Much of this had to do with his last statements, which seemed to suggest that a defining characteristic of such a state was simultaneous permutation symmetry in one-body and many-body spaces. In other words, that the state transforms as the totally symmetric representation of the symmetric (permutation) group in both the one-body and many-body spaces.

    For some reason, it was easier for me to see it in terms of permutation symmetry, rather than the usual statements about ordering and translational invariance. This is probably because, being trained in quantum chemistry, I am used to thinking about the symmetric group, but not used to thinking about translational invariance (molecules don't have this).

    After some thought and hand-waving in front of a mirror, I've convinced myself that this is probably a necessary consequence of the translational symmetry in an infinite system. If choosing a covering means choosing an origin, then all coverings must be equally weighted in the state.

    I have a wierd feeling that this has something to do with a paper that I found and haven't yet read, about how the symmetric group and the general linear group are dual to one another. Maybe I should bump that up the list.

  2. Hi Ross,

    Bruce's review is very nice indeed. Too bad it's published in an obscure journal and is not available on the arXiv. Among other things, Bruce shows an artist's rendition of spinons in a Heisenberg antiferromagnet on kagome.

    Here is my take on those spinons: arXiv:0902.0378