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This research establishes a tenfold classification for the symmetry and topology of monitored free fermions, revealing how measurement-induced dynamics create phenomena absent in closed quantum systems. By linking spacetime topology to specific boundary states like chiral edge modes, the study provides critical theoretical tools for understanding topological protection against dynamical purification.
Symmetry and Topology of Monitored Quantum Dynamics
arXiv:2412.06133v4 Announce Type: replace-cross Abstract: The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective non-Hermitian dynamical generators, thereby establishing the tenfold classification for symmetry and topology of monitored free fermions. Our classification elucidates the role of topology in measurement-induced phase transitions and identifies potential topological terms in the corresponding nonlinear sigma models. Furthermore, we establish the bulk-boundary correspondence in monitored quantum dynamics: nontrivial topology in spacetime manifests itself as topologically nontrivial steady states and gapless boundary states in Lyapunov spectra, such as Lyapunov zero modes and chiral edge modes, leading to the topologically protected slowdown of dynamical purification.
Abstract:The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective non-Hermitian dynamical generators, thereby establishing the tenfold classification for symmetry and topology of monitored free fermions. Our classification elucidates the role of topology in measurement-induced phase transitions and identifies potential topological terms in the corresponding nonlinear sigma models. Furthermore, we establish the bulk-boundary correspondence in monitored quantum dynamics: nontrivial topology in spacetime manifests itself as topologically nontrivial steady states and gapless boundary states in Lyapunov spectra, such as Lyapunov zero modes and chiral edge modes, leading to the topologically protected slowdown of dynamical purification.
Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Physics (quant-ph)
arXiv:2412.06133 [cond-mat.stat-mech]
(or arXiv:2412.06133v4 [cond-mat.stat-mech] for this version)
Phys. Rev. B 113, 134307 (2026)
https://doi.org/10.1103/1q83-jcbw DOI(s) linking to related resources
Full text under the publisher's open licence · 149 words
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