Breaking time-translation symmetry in nonunitary Gaussian circuits yields a fractal critical phase with tunable logarithmic entanglement growth, while specially designed random circuits keep robust volume-to-area transitions.
II is through the non-unitary op- erator UX (iλ), which models measuring ancilla qubits coupled to the spin chain at each site with strengthλ, and postselecting the outcome
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Entanglement transitions in structured and random nonunitary Gaussian circuits
Breaking time-translation symmetry in nonunitary Gaussian circuits yields a fractal critical phase with tunable logarithmic entanglement growth, while specially designed random circuits keep robust volume-to-area transitions.