Angelo Lucia

OS Mathematical Physics November 4 16:00

Thermalization in Kitaev’s quantum double models

Is it possible to have a 2D self-correcting memory? The general belief that this is not the case usually lies upon the absence of a strong enough energy barrier preventing errors and noise to quickly destroy the information encoded in the memory. But this is not sufficient, as there are entropic factors at play that could take the role of the energy barrier, by delaying the spread of errors. In order to really settle the question, one should look directly at the time required for the memory to thermalize.

In this talk, I will consider Kitaev's Quantum Double models with arbitrary group (including the non-abelian case). I will present a recent work in which, using tensor network techniques, we are able to prove that the thermalization dynamic given by Davies' generators has a spectral gap, therefore excluding the possibility of self-correction for this class of models.

Based on joint work with David Pérez-García and Antonio Pérez-Hernández. arxiv:2107.01628