Entanglement Complexity and Scrambling via Braiding of Nonabelions

Speaker: Zhicheng Yang, Boston University, Physics Department

When: January 28, 2019 (Mon), 01:00PM to 02:00PM (add to my calendar)
Location: SCI 352

This event is part of the Departmental Seminars.

Dissertation Committee: Claudio Chamon, Andrei Ruckenstein, Anatoli Polkovnikov, So-Young Pi, Michael El-Batanouny

Abstract: Scrambling is usually characterized by local entropy production under time evolution. However, scrambling can exhibit different complexities depending on the degree of randomness it produces, and there is a gap between maximal entanglement and complete randomization. We propose a measure of the degree of scrambling beyond entropic diagnostics by studying the entanglement spectrum (ES) statistics. I will first present concrete examples in random unitary circuits and Hamiltonian systems, where this entanglement complexity can be detected via the ES. I will further apply this measure to random braids of non-Abelian anyons and demonstrate that the ES reveals a hierarchy of scrambling among different systems even for the same amount of entanglement entropy.