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 the perturbation theory and isotropic entanglement theory.

arXiv comment5 pages, 3 figures, submitted to Phys. Rev. Lett

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• Accurate densities of states for disordered systems from free probability: Live Free or Diagonalize
• Eigenpairs of Toeplitz and disordered Toeplitz matrices with a Fisher-Hartwig symbol
• Partial freeness of random matrices
• Eigenvalue approximation of sums of Hermitian matrices from eigenvector localization/delocalization