Duality in power-law localization in disordered one-dimensional systems

X. Deng; V. E. Kravtsov; G. V. Shlyapnikov; L. Santos

doi:10.1103/physrevlett.120.110602

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arXiv · 1706.04088

Duality in power-law localization in disordered one-dimensional systems

X. Deng·V. E. Kravtsov·G. V. Shlyapnikov·L. Santos

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Abstract

The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, $1/r^a$. For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of $a>0$. Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops ($a<1$) and short-range hops ($a>1$) in which the wave function amplitude falls off algebraically with the same power $\gamma$ from the localization center.

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X. Deng, V. E. Kravtsov, G. V. Shlyapnikov, L. Santos. 2017-06-13. Duality in power-law localization in disordered one-dimensional systems. https://doi.org/10.1103/physrevlett.120.110602

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