Corrections to the Bethe lattice solution of Anderson localization
Matilde Baroni, Giulia Garcia Lorenzana, Tommaso Rizzo, Marco Tarzia
Abstract
Anderson localization is a fundamental phenomenon in condensed matter physics, with strong connections with many-body localization and quantum chaos. A crucial theoretical problem is that its behavior on the Bethe lattice, an infinite loop-less tree, differs dramatically from realistic models in finite dimensions. To amend the theory, the authors study here tree-like lattices with one loop of arbitrary length. The outcome opens the way to the computation of the critical exponents and explains some puzzling finite-size effects observed in numerical simulations.
Topics & Concepts
Bethe latticeLattice (music)Anderson localizationStatistical physicsPhysicsCondensed matter physicsAcousticsIsing modelQuantum many-body systemsModel Reduction and Neural NetworksAlgebraic structures and combinatorial models