Competition between unitary dynamics that scrambles quantum information non-locally and local measurements that probe and collapse the quantum state can result in a measurement-induced entanglement phase transition. Here we introduce analytically tractable models of measurement-induced criticality in large-N Brownian hybrid circuit model composed of qubits [1]. The system is initially entangled with an equal sized reference, and the subsequent hybrid system dynamics either partially preserves or totally destroys this entanglement depending on the measurement rate. Our approach can access a variety of entropic observables, which are represented as a path integral coupling four replicas with twisted boundary conditions. Saddle-point analysis reveals a second-order phase transition corresponding to replica permutation symmetry breaking below a critical measurement rate. The transition is mean-field-like and we characterize the critical properties near the transition in terms of a simple Ising field theory in 0+1 dimensions. We also extend these solvable models to study the effects of power-law long-range couplings on measurement-induced phases. In one dimension, the long-range coupling is irrelevant for α>3/2, with α being the power-law exponent. For α<3/2 the long-range coupling becomes relevant, leading to a nontrivial dynamical exponent at the measurement-induced phase transition. More interestingly, for α<1 the entanglement pattern receives a sub-volume correction for both area-law and volume-law phases. The volume-law phase with such a sub-volume correction realizes a novel quantum error correcting code whose code distance scales as L^(2−2α) [2].

References: [1] Phys. Rev. B 104, 094304 (2021), ArXiv:2104.07688., [2] ArXiv:2109.00013.

Pizza and drinks served after the talk.