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Quantum Institute: Visitor Schedule
The Quantum Lunch is regularly held on Thursdays in the Theoretical Division Conference Room, TA-3, Building 123, Room 121. For more information, contact Diego Dalvit.
May 11, 2006
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.