Video URL http://pirsa.org/21110031
Competition between unitary dynamics that scramble quantum information non-locally and local measurements that probe and collapse the quantum state can result in a measurement-induced entanglement phase transition. We introduce large-N Brownian hybrid circuits acting on clusters of qubits, which provide an analytically tractable model for measurement-induced criticality. The system is initially entangled with an equal sized reference, and the subsequent hybrid system dynamics either partially preserves or destroys this entanglement depending on the measurement rate. Our approach can access a variety of entropic observables, which are represented as a replica path integral 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. By coupling the large-N clusters on a lattice, 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 relevant for α<3/2, with α being the power-law exponent, 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 for α<1 realizes a novel quantum error correcting code whose code distance scales as L^(2−2α).
 Phys. Rev. B 104, 094304 (2021), ArXiv:2104.07688.