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Non-power-law universality in one-dimensional quasicrystals

Accepted version
Peer-reviewed

Type

Article

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Authors

Szabo, Attila 

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 β describing incommensurability in the system. This dependence is, however, found to be universal between a range of models sharing the same value of β. 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.

Description

Keywords

cond-mat.dis-nn, cond-mat.dis-nn, cond-mat.quant-gas, cond-mat.stat-mech, physics.atom-ph, quant-ph

Journal Title

PHYSICAL REVIEW B

Conference Name

Journal ISSN

2469-9950
2469-9969

Volume Title

98

Publisher

American Physical Society (APS)
Sponsorship
Engineering and Physical Sciences Research Council (EP/P009565/1)
European Research Council (716378)