From: Brenda Cook (brenda@math.missouri.edu)
Date: Wed Feb 07 2007 - 11:37:02 CST
COLLOQUIUM
University of Missouri-Columbia
Department of Mathematics
Robert Sims
University of California, Davis
Lieb-Robinson Bounds
and Related Results
Abstract: Locality in quantum spin systems can be described in terms of
a bound on the commutator of local observables with disjoint supports.
The first proof of such estimates was given by Lieb and Robinson in
1972. In my talk, I will discuss a generalization of these results and a
variety of applications. For example, these new results imply the
existence of the dynamics for a wider class of interactions, a bound on
the propagation of correlations through the system, and a proof of
exponential decay of (spatial) correlations in the ground state of
gapped Hamiltonians. Moreover, combining the above mentioned
applications, we were recently able to prove a multi-dimensional
Lieb-Schultz-Mattis theorem concerning the existence of low-lying
excitations for the spin-1/2 antiferromagnetic Heisenberg model.
3:30 p.m.
Thursday, February 8
114 General Classroom Building
Refreshments will be served at 2:45 p.m. in Room 326 Mathematical
Sciences (Math Lounge).
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