Renormalization approach to quasiperiodic tight binding models

Jukka A. Ketoja; Indubala I. Satij

doi:10.1016/0375-9601(94)00709-X

Renormalization approach to quasiperiodic tight binding models

Jukka A. Ketoja^*
, Indubala I. Satij

^*Corresponding author for this work

Not published at VTT

University of Helsinki
George Mason University

Research output: Contribution to journal › Article › Scientific › peer-review

18 Citations (Scopus)

Abstract

Tight binding models such as the Harper equation exhibiting the localization transition are studied using a nonperturbative renormalization method. The self-similarity underlying the fractal wave function is described by an infinite set of universal scaling ratios. Our studies confirm the existence of a fat critical phase in perturbed Harper models describing quantum spin chains and shows the existence of two new universality classes. Furthermore, the decimation scheme proposed here provides a new method for finding the minimum and the maximum energy eigenvalues up to machine precision.

Original language	English
Pages (from-to)	64-70
Number of pages	7
Journal	Physics Letters A
Volume	194
Issue number	1-2
DOIs	https://doi.org/10.1016/0375-9601(94)00709-X
Publication status	Published - 24 Oct 1994
MoE publication type	Not Eligible

Funding

The research of I.I.S. was supported by a grant from National Science Foundation DMR 093296. J.A.K. is grateful for the hospitality during his visit to the George Mason University, where this work was initiated.

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10.1016/0375-9601(94)00709-X

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AB - Tight binding models such as the Harper equation exhibiting the localization transition are studied using a nonperturbative renormalization method. The self-similarity underlying the fractal wave function is described by an infinite set of universal scaling ratios. Our studies confirm the existence of a fat critical phase in perturbed Harper models describing quantum spin chains and shows the existence of two new universality classes. Furthermore, the decimation scheme proposed here provides a new method for finding the minimum and the maximum energy eigenvalues up to machine precision.

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Renormalization approach to quasiperiodic tight binding models

Abstract

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