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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

quant-phcond-mat.dis-nncond-mat.str-elSubmitted Jan 4, 2026• Announced Jan 6, 2026• 0 citations
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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 $\{ω_j\}$, 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.

Comments
8 pages, 3 figures, 23 figures in Supplementary Material

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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 {ωj}\{ω_j\}{ωj​}, 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 ω1ω_1ω1​, 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.
Entanglement entropy is a fundamental diagnostic for quantum chaos, typically exhibiting volume-law scaling in highly excited eigenstates of chaotic many-body systems. In this work, we present a striking counterexample: a Floquet-driven quantum many-body system with a Rydberg-like blockade that, despite being fully chaotic as indicated by its Wigner-Dyson level statistics and local thermalization, exhibits a strict area-law entanglement entropy. Specifically, the entanglement entropy of every Floquet eigenstate is bounded by ln2, independent of system size. We trace this anomaly to the specific Hilbert space structure imposed by the blockades, which restricts the Schmidt rank across a bipartition. Furthermore, we generalize this discovery by establishing a duality between constrained many-body Hamiltonians and single-particle quantum walks on median graphs, and we outline a general procedure for constructing systems with an entanglement entropy bounded by a predetermined constant. Our results demonstrate that entanglement entropy alone is an insufficient diagnostic of many-body quantum chaos and highlight the profound impact of Hilbert space geometry on quantum dynamics and thermalization.
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Understanding the nonequilibrium dynamics of isolated quantum many-body systems is a central goal of modern physics. Measuring genuine many-body correlations in quantum systems is central to this aim, while it remains a fundamental challenge for systems lacking individual addressability. We introduce a multidimensional correlation imprinting technique that encodes the structure of a many-body state into the temporal fluctuation spectrum of a local quantum probe. This allows direct measurement of arbitrary-order correlations in nonequilibrium quantum states. Using a nitrogen-vacancy center in diamond coupled to a ^{13}C nuclear spin bath, we experimentally reconstruct many-body correlation landscape to third order. Furthermore, by analyzing the spectral structure of correlation cumulants, we directly visualize the dynamics of quantum entanglement. Our Letter establishes a general approach to probing complex nonequilibrium phenomena and entanglement in quantum many-body systems at the nanoscale.
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