The one dimensional quantum Ising model is used in quantum statistical physics to model interracting particles on a discrete lattice. While the classical model (in one and two dimensions) has long been solved (its origin dates back to 1930's), its quasiperiodic analog (dating back about 25 years) is still a source of interesting problems. We shall discuss our solution to one such problem: we'll rigorously prove that the energy spectrum of the one dimensional quantum quasiperiodic Ising model is a Cantor set, as has been long believed, and discuss some of its properties.
This is the first in a series of two seminars dedicated to this topic. In this seminar we'll present the problem and set up the main ideas.