Geometric additivity of modular commutator for multipartite entanglement

• URL: http://arxiv.org/abs/2407.11130v2
• Date: Thu, 25 Jul 2024 05:37:39 GMT
• Title: Geometric additivity of modular commutator for multipartite entanglement
• Authors: Sung-Min Park, Isaac H. Kim, Eun-Gook Moon,
• Abstract summary: We unveil novel geometric properties of many-body entanglement via a modular commutator of two-dimensional gapped quantum many-body systems. We derive a curious identity for the modular commutators involving disconnected intervals in a certain class of conformal field theories.
• Score: 1.4323608697751051
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A recent surge of research in many-body quantum entanglement has uncovered intriguing properties of quantum many-body systems. A prime example is the modular commutator, which can extract a topological invariant from a single wave function. Here, we unveil novel geometric properties of many-body entanglement via a modular commutator of two-dimensional gapped quantum many-body systems. We obtain the geometric additivity of a modular commutator, indicating that modular commutator for a multipartite system may be an integer multiple of the one for tripartite systems. Using our additivity formula, we also derive a curious identity for the modular commutators involving disconnected intervals in a certain class of conformal field theories. We further illustrate this geometric additivity for both bulk and edge subsystems using numerical calculations of the Haldane and $\pi$-flux models.

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