Boundary transfer matrix spectrum of measurement-induced transitions

Abstract

Measurement-induced phase transitions (MIPTs) are known to be described by non-unitary conformal field theories (CFTs) whose precise nature remains unknown. Most physical quantities of interest, such as the entanglement features of quantum trajectories, are described by boundary observables in this CFT. We introduce a transfer matrix approach to study the boundary spectrum of this field theory, and consider a variety of boundary conditions. We apply this approach numerically to monitored Haar and Clifford circuits, and to the measurement-only Ising model where the boundary scaling dimensions can be derived analytically. Our transfer matrix approach provides a systematic numerical tool to study the spectrum of MIPTs.

17 pages, 12 figures, 1 table

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• Critical Properties of Weak Measurement Induced Phase Transitions in Random Quantum Circuits
• Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
• Measurement-Induced Phase Transition in State Estimation of Chaotic Systems and the Directed Polymer
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models
• Random Quantum Circuits with Time-Reversal Symmetry
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• Monitored Fluctuating Hydrodynamics
• Transitions of the Lyapunov spectrum and entanglement entropy in monitored quantum dynamics with homogeneous unitary gates
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions