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Title: Subsystem symmetry, spin-glass order, and criticality from random measurements in a two-dimensional Bacon-Shor circuit
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.  more » « less
Award ID(s):
2110250
PAR ID:
10552756
Author(s) / Creator(s):
; ;
Publisher / Repository:
APS
Date Published:
Journal Name:
Physical Review B
Volume:
108
Issue:
2
ISSN:
2469-9950
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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