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Geometric additivity of modular commutator for multipartite entanglement
- Publication Year :
- 2024
-
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.<br />Comment: 4+8 pages, 6+10 figures, v2: updated references
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2407.11130
- Document Type :
- Working Paper