Renormalization to localization without a small parameter

Kutlin, Anton; Khaymovich, Ivan M.

doi:10.21468/SciPostPhys.8.4.049

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Renormalization to localization without a small parameter

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Kutlin, Anton
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Khaymovich, Ivan M.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Kutlin, A., & Khaymovich, I. M. (2020). Renormalization to localization without a small parameter. SciPost Physics, 8(4): 049. doi:10.21468/SciPostPhys.8.4.049.

Cite as: https://hdl.handle.net/21.11116/0000-0006-9EF9-0

Abstract

We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances. Due to generality of this model usually called Euclidean random matrix model, it arises naturally in various physical contexts such as studies of vibrational modes, artificial atomic systems, liquids and glasses, ultracold gases and photon localization phenomena. We generalize the known Burin-Levitov renormalization group approach, formulate universal conditions sufficient for localization in such models and inspect a striking equivalence of the wave function spatial decay between Euclidean random matrices and translation-invariant long-range lattice models with a diagonal disorder.