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.
Consequently, a (sub)volume law phase exists foranyrandomsequencealternatingbetween ˜U+ and ˜U−, which in turn imposes a dipolar random sequence on the operators U+ and U−
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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.