Sebastian Diehl
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. However, due to the stochastic nature of the wave function this type of phase transition does not manifest itself in common observable averages, obtained from the statistically averaged density matrix, and have instead mainly been observed in the dynamics entanglement.
Here we establish a novel type of entanglement transition between a regime of logarithmic entanglement growth, and a quantum Zeno regime obeying an area law, in continuously monitored fermion dynamics. We analyze the phase transition from different perspectives, via numerical simulations of monitored lattice fermions, and via analytical construction of an effective field theory for monitored Dirac fermions. In particular, we identify the relevant degrees of freedom for describing the phase transition, and show that their dynamics is governed by a non-Hermitian quantum Sine-Gordon model. This yields a physical picture for the phase transition in terms of a depinning from the measurement operator eigenstates induced by unitary dynamics, and places it into the BKT universality class.