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

Monday 23rd March 2015 - 16:00 to 17:00
INI Seminar Room 1
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons