Non-power-law universality in one-dimensional quasicrystals

Article

关键词: PERIODIC CORRECTIONS;    ENERGY-SPECTRUM;    WAVE-FUNCTIONS;    LOCALIZATION;    ELECTRON;    DYNAMICS;    EQUATION;    LATTICES;    PACKETS;    SYSTEMS;   

DOI  :  10.1103/PhysRevB.98.134201

来源: SCIE

【 摘 要 】

We have investigated scaling properties of the Aubry-Andre model and related one-dimensional quasiperiodic Hamiltonians near their localization 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 behavior 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-Andre model, we explain this behavior in terms of a discrete renormalization group protocol which predicts rich critical behavior. This result is complemented by studies of the expansion dynamics of a wave packet under the Aubry- Andre model at the critical point. Anomalous diffusion exponents are derived in terms of multifractal (Renyi) 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.

【 授权许可】

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