Scale-Invariant Survival Probability at Eigenstate Transitions

Abstract

Understanding quantum phase transitions in highly excited Hamiltonian eigenstates is currently far from being complete. It is particularly important to establish tools for their characterization in time domain. Here we argue that a scaled survival probability, where time is measured in units of a typical Heisenberg time, exhibits a scale-invariant behavior at eigenstate transitions. We first demonstrate this property in two paradigmatic quadratic models, the one-dimensional Aubry-Andre model and three-dimensional Anderson model. Surprisingly, we then show that similar phenomenology emerges in the interacting avalanche model of ergodicity breaking phase transitions. This establishes an intriguing similarity between localization transition in quadratic systems and ergodicity breaking phase transition in interacting systems.

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• Scale-invariant critical dynamics at eigenstate transitions
• Hilbert space delocalization under random unitary circuits
• Many-Body Mobility Edge in Quantum Sun models
• Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
• Long-range spectral statistics of the Rosenzweig-Porter model
• Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
• Critical dynamics of long-range quantum disordered systems
• Spectral form factor and energy correlations in banded random matrices
• Re-entrant localization induced by short-range hopping in the fractal Rosenzweig-Porter Model
• Scaling theory of fading ergodicity
• Diagnosing quantum transport from wave function snapshots
• Critical quantum dynamics of observables at eigenstate transitions
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
• Loop Charges and Fragmentation in Pairwise Difference Conserving Circuits
• Universal Relation between Spectral and Wavefunction Properties at Criticality