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We study a 2D measurement-only random circuit motivated by the Bacon-Shor error correcting code. We find a rich phase diagram as one varies the relative probabilities of measuring nearest-neighbor Pauli XX and ZZ check operators. In the Bacon-Shor code, these checks commute with a group of stabilizer and logical operators, which therefore represent conserved quantities. Described as a subsystem symmetry, these conservation laws lead to a continuous phase transition between an X-basis and Z-basis spin-glass order. The two phases are separated by a critical point where the entanglement entropy between two halves of an L × L system scales as L ln L, a logarithmic violation of the area law. We generalize to a model where the check operators break the subsystem symmetries (and the Bacon-Shor code structure). In tension with established heuristics, we find that the phase transition is replaced by a smooth crossover, and the X - and Z -basis spin-glass orders spatially coexist. Additionally, if we approach the line of subsystem symmetries away from the critical point in the phase diagram, some spin-glass order parameters jump discontinuously. 

Abstract Evidence of fluctuations in transport have long been predicted in³He. They are expected to contribute only within 100μK ofT_cand play a vital role in the theoretical modeling of ordering; they encode details about the Fermi liquid parameters, pairing symmetry, and scattering phase shifts. It is expected that they will be of crucial importance for transport probes of the topologically nontrivial features of superfluid³He under strong confinement. Here we characterize the temperature and pressure dependence of the fluctuation signature, by monitoring the quality factor of a quartz tuning fork oscillator. We have observed a fluctuation-driven reduction in the viscosity of bulk³He, finding data collapse consistent with the predicted theoretical behavior.