MBL & computations Quizz

How does entanglement propagate in the MBL phase ?

• Slowlier than in SYK model

• Entanglement does not propagate

Overall these lectures on MBL are:

• Too easy

• Too hard

• at the right pace

• Mixed bad: some parts easy, some parts hard

Consider writing the Hamiltonian of the SYK model at finite number N of Majoran fermions as a matrix in the Dirac occupation number basis. How does the number of non-zero elements per line scale ?

• O(1)

Consider the SYK model at finite number N of Majorana fermions. What is the size of the Hilbert space?

• applies to all Hamiltonians as long as they have local correlations

• is violated by integrable systems

• scales as log(A) for a state localized on A basis states

Question on level spacing statistics. Which one(s) is (are) correct ?

• In Poisson statistics, eigenlevels attract each other

• For real symmetric matrices from the Gaussian ensemble, eigenlevels repulse each

Anderson localization

• is a purely quantum mechanical phenomenon

• is due to disorder

• requires entanglement between particles

We can distinguish Anderson from Many-Body Localization

• by looking at imbalance after a quench

• by looking at entanglement dynamics after a quench

• from spectral statistics

• we can't