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TT: Fachverband Tiefe Temperaturen
TT 17: Quantum Manybody Systems (joint session QI/TT)
TT 17.8: Vortrag
Montag, 9. März 2026, 17:30–17:45, BEY/0245
Typical entanglement entropy of anyon chains — Yale Yauk1,2, •Alexander Hahn1,3,2, and Lucas Hackl4,5 — 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany — 2Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799 Munich, Germany — 3Technical University of Munich, TUM School of Natural Sciences, Physics Department, D-85748 Garching, Germany — 4School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia — 5School of Physics, The University of Melbourne, Parkville, VIC 3010, Australia
Random-state entanglement serves as a key probe of quantum chaos, thermalization, and information scrambling, but its behavior in topologically ordered systems remains unclear. Here we study the statistical properties of bipartite entanglement in one-dimensional anyon chains, where the Hilbert space is constrained by the fusion rules. In such systems, the conventional trace must be replaced by the quantum trace, requiring a consistent redefinition of density matrices and entanglement measures that incorporates topological data. We compute the average bipartite entanglement entropy and its variance for both open and periodic boundary conditions. The resulting average anyonic entanglement entropy reproduces the Page curve exactly, revealing that topological constraints modify the normalization but not the universal form of typical entanglement. Despite topological charge conservation, the average entanglement shows no symmetry-related correction of the kind that appears in systems with Lie group symmetries.
Keywords: Anyons and topological order; Entanglement; Categorical symmetries; Page curve; Quantum information