ABSTRACT
Matthew Hastings, Los Alamos National Laboratory
"Lieb-Schultz-Mattis in Higher Dimensions"
In 1961, Lieb, Schultz, and Mattis showed the absence of a gap in a
class of one-dimensional spin chains: chains with half-integer spin per
unit cell and SU(2)-invariant short-range interactions. This basic
result has guided research on spins chains ever since. For example, the
discovery of the Haldane gap in chains with integer spin was surprising
as it indicated a fundamental difference between integer and
half-integer spins. Since then, there has been much work searching for
higher dimensional extensions of this result, in particular due to
possible connections to high-temperature superconductivity. The
clearest statement of the basic physical reasons to expect such an
extension are due to Misguich et. al, who argued that any such system
would either have long-range spin order, and hence have gapless spin
wave excitations, or else would have a class of topological excitations
with vanishing gap. Thus, showing this result in higher dimensions
would connect directly to recent ideas on topological order in quantum
systems. I will sketch my recent proof of this result, emphasizing
connections to these basic physical ideas. In the process, I will
derive various results about locality of correlation functions in these
systems.
Thursday
May 27, 2004
4:10 pm, 416 Phy/Geo