Structured volume-law entanglement in an interacting, monitored Majorana spin liquid

Monitored quantum circuits allow for unprecedented dynamical control of many-body entanglement. Here we show that random, measurement-only circuits, implementing the competition of bond and plaquette couplings of the Kitaev honeycomb model, give rise to a structured volume-law entangled phase with subleading <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>L</a:mi><a:mo form="prefix">ln</a:mo><a:mi>L</a:mi></a:mrow></a:math> liquid scaling behavior. This interacting Majorana liquid takes up a highly symmetric, spherical parameter space within the entanglement phase diagram obtained when varying the relative coupling probabilities. The sphere itself is a critical boundary with quantum Lifshitz scaling separating the volume-law phase from proximate area-law phases, a color code or a toric code. An exception is a set of tricritical, self-dual points exhibiting effective <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mo>(</c:mo><c:mn>1</c:mn><c:mo>+</c:mo><c:mn>1</c:mn><c:mo>)</c:mo><c:mo>d</c:mo></c:math> conformal scaling at which the volume-law phase and both area-law phases meet. From a quantum information perspective, our results define error thresholds for the color code in the presence of projective error and stochastic syndrome measurements. Published by the American Physical Society 2024