# Vincenzo Alba: Diffusion and operator entanglement spreading

Source: Mathematical physics seminar

**Vincenzo Alba*** (University of Amsterdam***)**

I will discuss the dynamics of operator space entanglement entropy (OSEE) in integrable models. In particular, I will focus on the rule 54 chain and the XXZ chain, discussing the relationship between OSEE and diffusion. I will discuss the bound 1/2ln(t) for the OSEE of some simple, i.e., low-rank, diagonal local operators. I will provide numerical evidence that the bound is saturated in the rule 54 chain, and, remarkably, in the spin-1/2 Heisenberg XXZ chain. Finally, I will focus on the effect of integrability breaking, showing that strong finite-time effects are present in generic systems, which prevent from probing the asymptotic behavior of the OSEE.

**Zoom link:**

https://fmf-uni-lj-si.zoom.us/j/99208844366?pwd=Mm9Xa3F1Nzl6emExNEZ6UGpqTEFiUT09

Meeting ID: 973 3107 0547

Password: 808995