title: Error analysis of free probability approximations to the density of states of disordered systems.
abstract: Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble-averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with perturbation theory and isotropic entanglement theory.
authors.affiliation: Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA. jiahao@mit.edu
authors.forename: Jiahao
authors.initials: J
authors.lastname: Chen
authors.forename: Eric
authors.initials: E
authors.lastname: Hontz
authors.forename: Jeremy
authors.initials: J
authors.lastname: Moix
authors.forename: Matthew
authors.initials: M
authors.lastname: Welborn
authors.forename: Troy
authors.initials: T
authors.lastname: Van Voorhis
authors.forename: Alberto
authors.initials: A
authors.lastname: Suárez
authors.forename: Ramis
authors.initials: R
authors.lastname: Movassagh
authors.forename: Alan
authors.initials: A
authors.lastname: Edelman