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 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.

8+12 pages, 6 figures, v2 close to published version

References in corpus (4)

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• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Critical properties of the measurement-induced transition in random quantum circuits
• Competition between Chaotic and Non-Chaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model

Cited by in corpus (16)

• Nonlinear sigma models for monitored dynamics of free fermions
• Disordered monitored free fermions
• Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with $U(1)$ symmetry
• Universal KPZ scaling in noisy hybrid quantum circuits
• Entanglement Structure and Information Protection in Noisy Hybrid Quantum Circuits
• Noise-induced phase transitions in hybrid quantum circuits
• Universal Properties of the Spectral Form Factor in Open Quantum Systems
• Strong-to-weak Symmetry Breaking and Entanglement Transitions
• Onset of scrambling as a dynamical transition in tunable-range quantum circuits
• Phase transitions in sampling and error correction in local Brownian circuits
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Efficient circular Dyson Brownian motion algorithm
• Quantum conditional mutual information as a probe of measurement-induced entanglement phase transitions
• Noisy Monitored Quantum Circuits
• Robustness of a state with Ising topological order against local projective measurements
• Many-body spectral transitions through the lens of the variable-range SYK2 model