Bond Additivity and Persistent Geometric Imprints of Entanglement in Quantum Thermalization

TL;DR

This paper introduces a new framework called multi-bipartition entanglement tomography to analyze the geometric structure of entanglement in quantum many-body systems, revealing a bond-additive law and distinguishing thermalization mechanisms.

Contribution

It presents the bond-additive law and entanglement bond tensions as novel tools for probing entanglement geometry, and applies them to different quantum dynamics to uncover fundamental differences.

Findings

Entanglement entropy decomposes into bulk and geometric contributions.

Hamiltonian thermalized states retain a persistent geometric imprint.

Random circuits and Floquet dynamics erase the geometric structure.

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.