1. Geometric additivity of modular commutator for multipartite entanglement
- Author
-
Park, Sung-Min, Kim, Isaac H., and Moon, Eun-Gook
- Subjects
Quantum Physics ,Condensed Matter - Strongly Correlated Electrons ,High Energy Physics - Theory - 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., Comment: 4+8 pages, 6+10 figures, v2: updated references
- Published
- 2024