Probability and Stochastic Processes Seminar

Speaker: Christoph Fischbacher (University of California, Irvine)

Title: The Heisenberg XXZ model on the infinite chains

Abstract: We discuss the Heisenberg XXZ model on the infinite chain. We will show that the Hamiltonian can be transformed to an infinite direct sum of many-particle Schroedinger operators with attractive interaction potential energetically favoring clustered configurations. Using the Bethe ansatz, it can be shown that the lowest spectral band above the grand state is absolutely continuous. After this, we discuss what happens if a random magnetic background field is added and several open interesting questions.