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

• URL: http://arxiv.org/abs/2109.00013v3
• Date: Fri, 9 Dec 2022 17:22:56 GMT
• Title: Entanglement Phases in large-N hybrid Brownian circuits with long-range couplings
• Authors: Subhayan Sahu, Shao-Kai Jian, Gregory Bentsen, Brian Swingle
• Abstract summary: We develop solvable models of large-$N$ hybrid quantum circuits on qubits and fermions with long-range power-law interactions. We find that long-range free-fermionic circuits exhibit a distinct phase diagram with two different fractal entangled phases.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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