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  • Letter
  • Open Access

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

Guo-Yi Zhu1,2,*, Nathanan Tantivasadakarn3, and Simon Trebst1

  • *Contact author: guoyizhu@hkust-gz.edu.cn
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Phys. Rev. Research 6, L042063 – Published 13 December, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042063

Abstract

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 LlnL 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 (1+1)d 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.

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Phys. Rev. Research 6, L042063– Published 13 December, 2024
  • Received 18 April 2023
  • Accepted 25 October 2024
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