paper

Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions

arXiv:2102.08381 · doi:10.1103/PhysRevX.11.041004

Abstract

A wave function exposed to measurements undergoes pure state dynamics, with deterministic unitary and probabilistic measurement induced state updates, defining a quantum trajectory. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. To access it despite the randomness of single quantum trajectories, we construct an -replica Keldysh field theory for the ensemble average of the -th moment of the trajectory projector. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely, while others can be cast into the form of pure state evolutions generated by an effective non-Hermitian Hamiltonian. This decoupling is exact for free theories, and useful for interacting ones. In particular, we study locally measured Dirac fermions in dimensions, which can be bosonized to a monitored interacting Luttinger liquid at long wavelengths. For this model, the non-Hermitian Hamiltonian corresponds to a quantum Sine-Gordon model with complex coefficients. A renormalization group analysis reveals a gapless critical phase with logarithmic entanglement entropy growth, and a gapped area law phase, separated by a Berezinskii-Kosterlitz-Thouless transition. The physical picture emerging here is a pinning of the trajectory wave function into eigenstates of the measurement operators upon increasing the monitoring rate.

21+9 pages, 6 figures

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