Topology and Spectrum in Measurement-Induced Phase Transitions

• URL: http://arxiv.org/abs/2412.11097v4
• Date: Wed, 04 Jun 2025 08:38:13 GMT
• Title: Topology and Spectrum in Measurement-Induced Phase Transitions
• Authors: Hisanori Oshima, Ken Mochizuki, Ryusuke Hamazaki, Yohei Fuji,
• Abstract summary: We propose a general framework based on Lyapunov analysis to characterize topological properties in monitored quantum systems.<n>We illustrate this framework by analyzing (1+1)-dimensional monitored circuits for Majorana fermions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Competition among repetitive measurements of noncommuting observables and unitary dynamics can give rise to a wide variety of entanglement phases. Here, we propose a general framework based on Lyapunov analysis to characterize topological properties in monitored quantum systems through their spectrum and many-body topological invariants. We illustrate this framework by analyzing (1+1)-dimensional monitored circuits for Majorana fermions, which are known to exhibit topological and trivial area-law entangled phases as well as a critical phase with sub-volume-law entanglement. Through the Lyapunov analysis, we identify the presence (absence) of edge-localized zero modes inside the bulk gap in the topological (trivial) 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 distinguishes the two area-law phases and dynamically characterizes the critical phase. Our framework thus provides a general route to extend the notion of bulk-edge correspondence to monitored quantum dynamics.

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