Topology and Spectrum in Measurement-Induced Phase Transitions

• URL: http://arxiv.org/abs/2412.11097v3
• Date: Mon, 23 Dec 2024 14:19:06 GMT
• Title: Topology and Spectrum in Measurement-Induced Phase Transitions
• Authors: Hisanori Oshima, Ken Mochizuki, Ryusuke Hamazaki, Yohei Fuji,
• Abstract summary: We characterize topological phases in monitored quantum systems by their spectrum and many-body topological invariants. Our work thus paves the way to extend the bulk-edge correspondence for topological phases from equilibrium to monitored quantum dynamics.
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• Abstract: Competition among repetitive measurements of noncommuting observables and unitary dynamics can give rise to a rich variety of entanglement phases. We here characterize topological phases in monitored quantum systems by their spectrum and many-body topological invariants. We analyze (1+1)-dimensional monitored circuits for Majorana fermions, which have topological and trivial area-law entangled phases and a critical phase with sub-volume-law entanglement, through the Lyapunov spectrum. We uncover the presence (absence) of edge-localized zero modes inside the bulk gap in the topological (trivial) area-law phase and a bulk gapless spectrum in the critical phase. Furthermore, by suitably exploiting the fermion parity with twisted measurement outcomes at the boundary, we construct a topological invariant that sharply distinguishes the two area-law phases and dynamically characterizes the critical phase. Our work thus paves the way to extend the bulk-edge correspondence for topological phases from equilibrium to monitored quantum dynamics.

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