Entanglement phases in large- N hybrid Brownian circuits with long-range couplings

Abstract

We develop solvable models of large-N hybrid quantum circuits on qubits and fermions with tunable long-range power-law interactions and continuous local monitoring. These models provide analytical access to the entanglement phase diagram and error-correcting properties of many-body entangled nonequilibrium states generated by such dynamics. In one dimension, the long-range couplings are irrelevant for α>3/2, where α is the power-law exponent, and the models exhibit a conventional measurement-induced phase transition between volume- and area-law entangled phases. For 1/2 <1, the entanglement pattern receives a subvolume correction for both area-law and volume-law phases, indicating that the phase realizes a quantum error correcting code whose code distance scales as L2-2α. While the entanglement phase diagram is the same for both the interacting qubit and fermionic hybrid Brownian circuits, we find that long-range free-fermionic circuits exhibit a distinct phase diagram with two different fractal entangled phases.