Random loop representations of quantum spin systems and their universal behaviour 1-2

03/10/2016 - 14:30
03/10/2016 - 17:00
Daniel Ueltschi, (University of Warwick)
McGill University, Department of Mathematics, 805 Sherbrooke St. West, Burnside Hall, Burn 1120

I will describe the representations of Tóth and Aizenman-Nachtergaele of quantum Heisenberg models. They constitute an example of “loop soup” models that display  a universal behaviour in dimensions 3 and higher: At low temperatures, the system contains macroscopic loops and the joint distribution of their lengths is given by a Poisson-Dirichlet distribution. This can be understood (and calculated) by viewing the loop distribution as the invariant measure of an effective spit-merge process.

I will explain the relevant notions. If time permits, I will derive some consequences of this universal behaviour regarding the nature of symmetry breaking in quantum spin systems.

Last edited by on Thu, 03/03/2016 - 15:15