Non-power-law universality in one-dimensional quasicrystals
| cam.issuedOnline | 2018-10-01 | |
| dc.contributor.author | Szabo, Attila | |
| dc.contributor.author | Schneider, Ulrich | |
| dc.contributor.orcid | Schneider, Ulrich [0000-0003-4345-9498] | |
| dc.date.accessioned | 2018-09-08T06:35:33Z | |
| dc.date.available | 2018-09-08T06:35:33Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract | We have investigated scaling properties of the Aubry-Andr\'e model and related one-dimensional quasiperiodic Hamiltonians near their localisation transitions. We find numerically that the scaling of characteristic energies near the ground state, usually captured by a single dynamical exponent, does not obey a power law relation. Instead, the scaling behaviour depends strongly on the correlation length in a manner governed by the continued fraction expansion of the irrational number $\beta$ describing incommensurability in the system. This dependence is, however, found to be universal between a range of models sharing the same value of $\beta$. For the Aubry-Andr\'e model, we explain this behaviour in terms of a discrete renormalisation group protocol which predicts rich critical behaviour. This result is complemented by studies of the expansion dynamics of a wave packet under the Aubry-Andr\'e model at the critical point. Anomalous diffusion exponents are derived in terms of multifractal (R\'enyi) dimensions of the critical spectrum; non-power-law universality similar to that found in ground state dynamics is observed between a range of critical tight-binding Hamiltonians. | |
| dc.identifier.doi | 10.17863/CAM.27314 | |
| dc.identifier.eissn | 2469-9969 | |
| dc.identifier.issn | 2469-9950 | |
| dc.identifier.uri | https://www.repository.cam.ac.uk/handle/1810/279946 | |
| dc.language.iso | eng | |
| dc.publisher | American Physical Society (APS) | |
| dc.publisher.url | http://dx.doi.org/10.1103/PhysRevB.98.134201 | |
| dc.subject | cond-mat.dis-nn | |
| dc.subject | cond-mat.dis-nn | |
| dc.subject | cond-mat.quant-gas | |
| dc.subject | cond-mat.stat-mech | |
| dc.subject | physics.atom-ph | |
| dc.subject | quant-ph | |
| dc.title | Non-power-law universality in one-dimensional quasicrystals | |
| dc.type | Article | |
| dcterms.dateAccepted | 2018-08-28 | |
| prism.issueIdentifier | 13 | |
| prism.number | ARTN 134201 | |
| prism.publicationDate | 2018 | |
| prism.publicationName | PHYSICAL REVIEW B | |
| prism.volume | 98 | |
| pubs.funder-project-id | Engineering and Physical Sciences Research Council (EP/P009565/1) | |
| pubs.funder-project-id | European Research Council (716378) | |
| rioxxterms.licenseref.startdate | 2018-10-01 | |
| rioxxterms.licenseref.uri | http://www.rioxx.net/licenses/all-rights-reserved | |
| rioxxterms.type | Journal Article/Review | |
| rioxxterms.version | AM | |
| rioxxterms.versionofrecord | 10.1103/PhysRevB.98.134201 |
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