Anomalies of average symmetries: entanglement and open quantum systems

• Published in: The journal of high energy physics Vol. 2024; no. 10; pp. 134 - 42
• Main Authors: Hsin, Po-Shen, Luo, Zhu-Xi, Sun, Hao-Yu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 18.10.2024; Springer Nature B.V; SpringerOpen
• Subjects: Anomalies; Classical and Quantum Gravitation; Commutation; Constraints; Density; Discrete Symmetries; Eigenvalues; Elementary Particles; Global Symmetries; Lower bounds; Many body problem; Phase transitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Symmetry; t Hooft and Polyakov loops; Topological States of Matter; Wilson; Discrete Symmetries; Global Symmetries; Wilson; t Hooft and Polyakov loops; Topological States of Matter
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2024)134

A bstract Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on average. This work investigates the constraints on mixed states resulting from non-commuting average symmetries. We will focus on the cases where the commutation relations of the average symmetry generators are violated by nontrivial phases, and call such average symmetry anomalous. We show that anomalous average symmetry implies degeneracy in the density matrix eigenvalues, and present several lattice examples with average symmetries, including XY chain, Heisenberg chain, and deformed toric code models. In certain cases, the results can be further extended to reduced density matrices, leading to a new lower bound on the entanglement entropy. We discuss several applications in the contexts of many body localization, quantum channels, entanglement phase transitions and also derive new constraints on the Lindbladian evolution of open quantum systems.