Entanglement Spectrum in Quantum Many-Body Dynamics and Braiding of Non-Abelian Anyons
This event is part of the Condensed Matter Theory Seminar Series.
We study the entanglement spectrum of highly entangled states in two different contexts: (1) time evolved states after a quantum quench with Hamiltonians exhibiting different dynamical phases; (2) braiding of non-abelian anyons capable or not of universal quantum computation. In the first case, we show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns in the entanglement spectrum after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermalization, albeit within very different time scales. We further show that the complexity of entanglement, revealed by the possibility of disentangling the state through a Metropolis-like algorithm, is signaled by whether the entanglement spectrum is Poisson or Wigner-Dyson. In the second part, we study the entanglement spectrum of states generated out of braiding two types of non-abelian anyons: the Majorana fermions and the Fibonacci anyons. We show that the information on whether certain representations of the braid group associated with non-abelian anyons are capable of universal quantum computation can also be extracted from the entanglement spectrum.