Hierarchical entanglement transitions and hidden area-law sectors in quantum many-body dynamics
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911652249600000 |
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| author | Grover, Tarun |
| author_facet | Grover, Tarun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04540 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hierarchical entanglement transitions and hidden area-law sectors in quantum many-body dynamics Grover, Tarun Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory 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. |
| title | Hierarchical entanglement transitions and hidden area-law sectors in quantum many-body dynamics |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.04540 |