Bond Additivity and Persistent Geometric Imprints of Entanglement in Quantum Thermalization

• URL: http://arxiv.org/abs/2601.01327v1
• Date: Sun, 04 Jan 2026 01:59:52 GMT
• Title: Bond Additivity and Persistent Geometric Imprints of Entanglement in Quantum Thermalization
• Authors: Chun-Yue Zhang, Shi-Xin Zhang, Zi-Xiang Li,
• Abstract summary: We introduce a powerful framework, termed multi-bi partition entanglement tomography.<n>Our cornerstone is the discovery of a bond-additive law''<n>We apply this framework to Hamiltonian dynamics, random quantum circuits, and Floquet dynamics.
• Score: 4.588127679007806
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\{ω_j\}$, 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 $ω_1$, 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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