Yagi, H., Mochizuki, K., & Gong, Z. (2024). Threefold Way for Typical Entanglement. arXiv preprint arXiv:2410.11309.
This paper aims to unveil the physical interpretation of the Laguerre symplectic ensemble (LSE) in the context of entanglement spectra, particularly in systems exhibiting half-integer-spin time-reversal symmetry where a direct analogue from Hamiltonian systems breaks down.
The authors utilize the concept of symmetry fractionalization, known from the study of topological phases, to construct a system where the global time-reversal symmetry is fractionalized on subsystems. They analyze the entanglement spectrum of random symmetric states in this system using tools from random matrix theory.
This work establishes a direct connection between the statistics of entanglement spectra in systems with symmetries and the Dyson's threefold way of random matrix theory. The study reveals the significance of symmetry fractionalization in characterizing entanglement properties and provides a framework for understanding the emergence of different random matrix ensembles in various physical systems.
This research significantly contributes to the understanding of entanglement in quantum systems with symmetries. It provides a new perspective on the classification of entanglement spectra and opens avenues for exploring the interplay between symmetry, topology, and entanglement.
The study focuses on 0-form invertible symmetries described by finite groups. Future research could explore extensions to continuous symmetries, higher-form symmetries, non-invertible symmetries, and fermionic systems with superselection rules. Investigating the implications of these findings for specific physical systems and their potential applications in areas like quantum information science would also be of great interest.
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by Haruki Yagi,... alle arxiv.org 10-16-2024
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