Dimerisation in mirror models and quantum spin chains

Jakob Björnberg, University of Gothenburg
Jadwin Hall A10

We consider two models of random loops where we prove breaking of translational symmetry. The first is a mirror model, where the loops are formed by light rays bouncing in a labyrinth of randomly oriented mirrors. The second is a probabilistic representation of a quantum spin chain, and can be obtained as a limit of the first, for inhomogeneous mirror weights. In the terminology of quantum spins, this symmetry-breaking is called “dimerisation”. Based on joint works with K. Ryan as well as with P. Muehlbacher, B. Nachtergaele and D. Ueltschi.