Hierarchical entanglement transitions and hidden area-law sectors in quantum many-body dynamics

TL;DR

This paper uncovers a hierarchical structure of entanglement transitions in quantum many-body dynamics, revealing area-law and volume-law regimes depending on the Renyi index, with implications for approximability and recursive entanglement features.

Contribution

It introduces a hierarchical entanglement structure in local quantum quenches, analytically derives the mechanism, and demonstrates the hierarchy through numerical and theoretical methods.

Findings

At long times, $S_{\alpha>1}$ obeys an area law, while $S_{\alpha\le 1}$ is volume-law.

The dominant Schmidt sector carries the linear response to quench strength and exhibits its own phase transition.

The hierarchical structure persists recursively upon bipartitioning the dominant Schmidt states.

Abstract

Chaotic many-body dynamics typically generates volume-law entanglement from initially low-entangled states. We reveal an intricate, hierarchical entanglement structure in local quantum quenches, both in the canonical purification of locally quenched Gibbs states and in a companion pure-state circuit model. In either setting, the full state exhibits a Renyi-index-tuned transition: at long times, $S_{\alpha>1}$ obeys an area law, while $S_{\alpha\le 1}$ is volume-law. More strikingly, the response linear in the quench strength is carried by only an O(1)-dimensional dominant Schmidt sector; the corresponding states exhibit their own area-to-volume-law transitions at critical indices $\alpha_c<1$, implying polynomial-bond-dimension approximability in one dimension. We provide evidence that this hierarchy persists recursively: upon bipartitioning the dominant Schmidt states, their leading Schmidt sectors exhibit analogous structure. We derive the mechanism analytically in the circuit model, prove the $S_{\alpha>1}$ area law for locally quenched Gibbs states, and support the hierarchy by exact diagonalization of random circuits and locally quenched Gibbs states of chaotic spin chains.