Scale-Invariant Survival Probability at Eigenstate Transitions

TL;DR

This paper demonstrates that the scaled survival probability exhibits scale-invariant behavior at eigenstate transitions across quadratic and interacting models, revealing a universal feature of quantum phase transitions in eigenstates.

Contribution

It introduces the concept of scale-invariant survival probability at eigenstate transitions and shows its applicability across different quantum models, including interacting systems.

Findings

Scale-invariant behavior observed in quadratic models.

Similar phenomenology found in interacting avalanche model.

Universal feature linking localization and ergodicity breaking 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.