Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs

Abstract

The scaling of the Thouless time with system size is of fundamental importance to characterize dynamical properties in quantum systems. In this work, we study the scaling of the Thouless time in the Anderson model on random regular graphs with on-site disorder. We determine the Thouless time from two main quantities: the spectral form factor and the power spectrum. Both quantities probe the long-range spectral correlations in the system and allow us to determine the Thouless time as the time scale after which the system is well described by random matrix theory. We find that the scaling of the Thouless time is consistent with the existence of a sub-diffusive regime anticipating the localized phase. Furthermore, to reduce finite-size effects, we break energy conservation by introducing a Floquet version of the model and show that it hosts a similar sub-diffusive regime.

9 pages, 7 figures, 118 references + 1 page, 3 figures in Appendices

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• Universality in Anderson localization on random graphs with varying connectivity
• Delayed Thermalization in Mass-Deformed SYK
• Analytic solution of the resolvent equations for heterogeneous random graphs: spectral and localization properties
• Power spectrum of the circular unitary ensemble
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Localization and fractality in disordered Russian Doll model