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 | |
| 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.