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 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.

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Cited by in corpus (17)

• Many-Body Localization in the Age of Classical Computing
• Proposal for many-body quantum chaos detection
• Normal weak eigenstate thermalization
• The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes
• Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
• Long-range spectral statistics of the Rosenzweig-Porter model
• Re-entrant localization induced by short-range hopping in the fractal Rosenzweig-Porter Model
• Spectral form factor and energy correlations in banded random matrices
• Scaling theory of fading ergodicity
• Diagnosing quantum transport from wave function snapshots
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Critical quantum dynamics of observables at eigenstate transitions
• Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
• Comparative Study of Indicators of Chaos in the Closed and Open Dicke Model
• Universal Relation between Spectral and Wavefunction Properties at Criticality
• Many-body spectral transitions through the lens of the variable-range SYK2 model