Speaker
Angelo Lucia, Politecnico di Milano
Abstract
There are physically motivated heuristic arguments that indicate that 2D topologically ordered spin models, whose elementary excitations are quasi-particles with anyonic exchange and braiding statistics, have fast thermalisation dynamics, i.e., that at any positive temperature they reach thermal equilibrium very quickly. I will present some recent results that go in the direction of rigorously proving that this is in fact the case.
Starting from a description of the thermalisation dynamics as an ergodic quantum Markov semigroup, whose mixing time can be controlled by estimating the spectral gap of its generator, I will consider the case of semigroups which satisfy a strong quantum detailed balance condition. For these generators, I will show how to estimate the spectral gap via a correlation decay measure on the Gibbs state. Examples of models for which the correlation decay can be explicitly computed are the 2D quantum double models by Kitaev with arbitrary group (including non-abelian cases).
Based on a joint work with D. Pérez-García and A. Pérez-Hernández (arXiv:2505.08991)