Localization transitions in quadratic systems without quantum chaos

TL;DR

This paper investigates localization transitions in quadratic 1D models, revealing complex behaviors where some measures suggest RMT-like universality at transition points, while others do not, indicating diverse entanglement properties.

Contribution

It uncovers unconventional localization transitions in quadratic models, showing partial RMT universality and diverse entanglement behaviors without quantum chaos.

Findings

Eigenstate entanglement entropy varies with bipartition, showing volume-law behavior.

Transition points exhibit mixed RMT-like and non-universal features.

Localization transitions occur without quantum chaos in quadratic models.

Abstract

Transitions from delocalized to localized eigenstates have been extensively studied in both quadratic and interacting models. The delocalized regime typically exhibits diffusion and quantum chaos, and its properties comply with the random matrix theory (RMT) predictions. However, it is also known that in certain quadratic models, the delocalization in position space is not accompanied by the single-particle quantum chaos. Here, we study the one-dimensional Anderson and Wannier-Stark models that exhibit eigenstate transitions from localization in quasimomentum space (supporting ballistic transport) to localization in position space (with no transport) in a nonstandard thermodynamic limit, which assumes rescaling the model parameters with the system size. We show that the transition point may exhibit an unconventional character of Janus type, i.e., some measures hint at the RMT-like universality emerging at the transition point, while others depart from it. For example, the eigenstate entanglement entropies may exhibit, depending on the bipartition, a volume-law behavior that either approaches the value of Haar-random Gaussian states, or converges to a lower, non-universal value. Our results hint at rich diversity of volume-law eigenstate entanglement entropies in quadratic systems that are not maximally entangled.