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arXiv · 2601.01327

Bond Additivity and Persistent Geometric Imprints of Entanglement in Quantum Thermalization

Chun-Yue Zhang·Shi-Xin Zhang·Zi-Xiang Li
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Abstract

Characterizing the intricate structure of entanglement in quantum many-body systems remains a central challenge, as standard measures often obscure underlying geometric details. In this Letter, we introduce a powerful framework, termed multi-bipartition entanglement tomography, which probes the fine structure of entanglement across an exhaustive ensemble of distinct bipartitions. Our cornerstone is the discovery of a ``bond-additive law'', which reveals that the entanglement entropy can be precisely decomposed into a bulk volume-law baseline plus a geometric correction formed by a sum of local contributions from crossed bonds of varying ranges. This law distills complex entanglement landscapes into a concise set of entanglement bond tensions $\{\omega_j\}$, serving as a quantitative fingerprint of interaction locality. By applying this tomography to Hamiltonian dynamics, random quantum circuits, and Floquet dynamics, we resolve a fundamental distinction between thermalization mechanisms: Hamiltonian thermalized states retain a persistent geometric imprint characterized by a significantly non-zero $\omega_1$, while this structure is completely erased in random quantum circuit and Floquet dynamics. Our work establishes multi-bipartition entanglement tomography as a versatile toolbox for the geometric structure of quantum information in many-body systems.

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Chun-Yue Zhang, Shi-Xin Zhang, Zi-Xiang Li. 2026-01-04. Bond Additivity and Persistent Geometric Imprints of Entanglement in Quantum Thermalization. https://arxiv.org/abs/2601.01327

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