Entanglement Phases in large-N hybrid Brownian circuits with long-range couplings
Subhayan Sahu, Shao-Kai Jian, Gregory S. Bentsen, Brian G. Swingle · arXiv (Cornell University) · 2021
We develop solvable models of large-$N$ hybrid quantum circuits on qubits and fermions with long-range power-law interactions and continuous local monitoring, which provide analytical access to the entanglement phase diagram and error-correcting properties of many-body entangled non-equilibrium states generated by such dynamics. In one dimension, the long-range coupling is 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 $1/2<α<3/2$ 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, indicating that the phase realizes a quantum error correcting code whose code distance scales as $L^{2-2α}$. 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.