Scale-invariant critical dynamics at eigenstate transitions

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 recent results [1,2,3], we
explore features of scale invariant dynamics of SFF and survival
probability 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 [4]. 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. Based on
empirical comparisons, we discuss universal trends in features of the
scale-invariant critical dynamics, which are expressed by smooth
functions of a tuning parameter [4].

[1] J. Šuntajs, T. Prosen, L. Vidmar, Ann. Phys. 435, 168469 (2021).
[2] J. Šuntajs and L. Vidmar, Phys. Rev. Lett. 129, 060602 (2022).
[3] M.Hopjan and L. Vidmar, Phys. Rev. Lett. 131, 060404 (2023).
[4] M.Hopjan and L. Vidmar, Phys. Rev. Res. 5, 043301 (2023)