Scale-invariant critical dynamics at eigenstate transitions

TL;DR

This paper investigates scale-invariant quantum dynamics at eigenstate transitions, revealing that criticality exhibits scale invariance at both late and mid-times across various models, extending understanding of quantum chaos and localization.

Contribution

It demonstrates that scale-invariant dynamics occur at critical eigenstate transitions at both late and mid-times, broadening the scope beyond traditional late-time behavior.

Findings

Scale invariance at criticality extends to mid-time dynamics.

Applicable to quadratic and interacting models.

Observed in multiple models including Anderson and Rosenzweig-Porter.

Abstract

The notion of scale-invariant dynamics is well established at late times in quantum chaotic systems, as illustrated by the emergence of a ramp in the spectral form factor (SFF). Building on the results of the preceding Letter [Phys. Rev. Lett. 131, 060404 (2023)], we explore features of scale-invariant dynamics of survival probability and SFF at criticality, i.e., at eigenstate transitions from quantum chaos to localization. We show that, in contrast to the quantum chaotic regime, the quantum dynamics at criticality do not only exhibit scale invariance at late times, but also at much shorter times that we refer to as mid-time dynamics. Our results apply to both quadratic and interacting models. Specifically, we study Anderson models in dimensions three to five and power-law random banded matrices for the former, and the quantum sun model and the ultrametric model for the latter, as well as the Rosenzweig-Porter model.