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

• URL: http://arxiv.org/abs/2605.04540v1
• Date: Wed, 06 May 2026 06:40:58 GMT
• Title: Hierarchical entanglement transitions and hidden area-law sectors in quantum many-body dynamics
• Abstract summary: Chaotic many-body dynamics typically generates volume-law entanglement from initially low-entangled states.<n>We reveal an intricate, hierarchical entanglement structure in local quantum quenches.<n>We derive the mechanism analytically in the circuit model, prove the $S_>1$ area law for locally quenched Gibbs states, and support the hierarchy by exact diagonalization of random circuits.
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• License: http://creativecommons.org/licenses/by/4.0/
• 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, $S_{α>1}$ obeys an area law, while $S_{α\le 1}$ 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 $α_c<1$, 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 $S_{α>1}$ 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.

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