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Entanglement in the disordered XY spin chain and open problems for random block operators

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Periodic and Ergodic Spectral Problems

Random block operators appear as effective one-particle Hamiltonians in the study of the anisotropic XY spin chain. We will discuss that dynamical localization of the effective Hamiltonian implies a uniform area law for the entanglement of all eigenstates of the XY chain in random field. An open problem in this context is the regularity of the Lyapunov exponents for the associated random block operators. A difficulty arises due to the break down of irreducibility of transfer matrices at zero energy.

This talk is part of the Isaac Newton Institute Seminar Series series.

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