Renormalization group and dynamical maps for the hierarchical tight-binding problem
Year: 1989
Authors: W�rtz D., Schneider T., Politi A., Zannetti M.
Autors Affiliation: IBM Research Division, Zurich Research Laboratory, 8803 R�schlikon, Switzerland;
Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy;
Interdisziplinares Projecktzentrum fur Supercomputing, Zurich, Switzerland;
Dip. di Fisica, Universit� di Salerno Italy
Abstract: A tight-binding model in one dimension with hierarchical potential strength is investigated. The problem is reduced to three equivalent recursive relations: (i) for characteristic polynomials, (ii) for a renormalization-group transformation, and (iii) for traces of transfer matrices. On this basis, the nature of the energy spectrum and the character of the wave functions is elucidated. The scaling properties are also analyzed in terms of the stability of fixed points, period two-cycles, and aperiodic solutions. For short chains, resistance and transmission are calculated as functions of system length and energy in view of experimental realizations.
Journal/Review: PHYSICAL REVIEW B
Volume: 39 (11) Pages from: 7829 to: 7839
KeyWords: tight-binding model
DOI: 10.1103/PhysRevB.39.7829
Citations: 20
data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2025-03-30
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