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arXiv · 2412.11097

Topology and Spectrum in Measurement-Induced Phase Transitions

Hisanori Oshima·Ken Mochizuki·Ryusuke Hamazaki·Yohei Fuji
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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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Hisanori Oshima, Ken Mochizuki, Ryusuke Hamazaki, Yohei Fuji. 2024-12-15. Topology and Spectrum in Measurement-Induced Phase Transitions. https://doi.org/10.1103/physrevlett.134.240401

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