Chebyshev-polynomial expansion of the localization length of Hermitian and non-Hermitian random chains

Abstract

We carry Chebyshev-polynomial expansion of the inverse localization length of Hermitian and non-Hermitian random chains as function of energy. For Hermitian models, the expansion produces numerically this energy-dependent function in one run of the algorithm. This is in strong contrast to the standard transfer-matrix method, which produces the inverse localization length for a fixed energy in each run. For non-Hermitian models, as in the transfer-matrix method, our algorithm computes the inverse localization length for a fixed (complex) energy. We also find a formula of the Chebyshev-polynomial expansion of the density of states of non-Hermitian models. As explained in more detail in the Introduction, our algorithm for non-Hermitian models may be the only available efficient algorithm for finding the density of states of models with interactions.

19 pages, 9 figures, to appear in Phys. Rev. E

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• Level statistics of real eigenvalues in non-Hermitian systems
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• Non-Unitary Quantum Many-Body Dynamics using the Faber Polynomial Method
• Probing Band-center Anomaly with the Kernel Polynomial Method
• Delocalization of non-Hermitian Quantum Walk on Random Media in One Dimension
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Chebyshev Polynomial Method to Landauer-Büttiker Formula of Quantum Transport in Nanostructures
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Anomalous Non-Hermitian Topological Anderson Insulator