## Abstract

We study Chebyshev-polynomial expansion of the inverse localization length of Hermitian and non-Hermitian random chains as a function of energy. For Hermitian models, the expansion produces this energy-dependent function numerically 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 detail, our algorithm for non-Hermitian models may be the only available efficient algorithm for finding the density of states of models with interactions.

Original language | English |
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Article number | 063305 |

Journal | Physical Review E |

Volume | 94 |

Issue number | 6 |

DOIs | |

State | Published - 19 Dec 2016 |

### Bibliographical note

Publisher Copyright:© 2016 American Physical Society.

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics