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

TL;DR

This paper develops solvable models of large-N hybrid quantum circuits with long-range interactions, revealing how the entanglement phase diagram and error correction properties depend on the power-law exponent, including new phases and critical behaviors.

Contribution

It introduces analytical models of long-range hybrid circuits that uncover the impact of power-law couplings on entanglement phases and error correction, including novel sub-volume entanglement corrections.

Findings

Long-range couplings are irrelevant for ta>3/2, showing a standard phase transition.

For 1/2<ta<3/2, long-range interactions alter the critical dynamics.

For ta<1, the phases exhibit sub-volume entanglement scaling and quantum error correction properties.

Abstract

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 $\alpha>3/2$, where $\alpha$ is the power-law exponent, and the models exhibit a conventional measurement-induced phase transition between volume- and area-law entangled phases. For $1/2<\alpha<3/2$ the long-range coupling becomes relevant, leading to a nontrivial dynamical exponent at the measurement-induced phase transition. More interestingly, for $\alpha<1$ 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 $L^{2-2\alpha}$. 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.