Michael Buchhold
A wave function exposed to measurements undergoes pure state dynamics, with deterministic unitary and probabilistic measurement-induced state updates. For many-particle systems, the competition of these different elements gives rise to a scenario similar to quantum phase transitions, which are visible in the entanglement structure of the wave functions. They are masked, however, in standard quantum mechanical observables due to the randomness of measurement outcomes. We study the dynamics of locally measured free fermions in (1+1) dimensions undergoing a measurement-induced phase transition. We strengthen the analogy between this transition and ground state quantum phase transitions by examining a replica field theory for the n-th moment of the measured wave function: the phase transition corresponds to a macroscopic change in the dark state wave function of a non-Hermitian Hamiltonian. In a second step, we introduce a general strategy to make measurement-induced transitions observable. It relies on breaking the measurement degeneracy explicitly by steering the system towards a chosen representative state. This strategy introduces a unique dark or absorbing state and creates a link of measurement-induced phase transitions to new forms of quantum absorbing state transitions, which can be detected by standard means via a local order parameter.