## 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

Funding Information:N.H. greatly appreciates the hospitality of Department of Physics, Technion, and particularly Prof. Dov Levine for the support of the stay. N.H.'s research is partially supported by Kakenhi Grants No. 15K05200, No. 15K05207, and No. 26400409 from Japan Society for the Promotion of Science.

Publisher Copyright:

© 2016 American Physical Society.

## ASJC Scopus subject areas

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