Intrinsic mixed state topological order in a stabilizer system under stochastic decoherence: Strong-to-weak spontaneous symmetry breaking from percolation point of view

Abstract

Discovering quantum orders in mixed many-body systems is an ongoing issue. Very recently, the notion of an intrinsic mixed state topologically-ordered (IMTO) state was proposed. As a concrete example, we observe the emergence of IMTO by studying the toric code system under stochastic maximal decoherence by $ZX$-diagonal type projective measurement without monitoring. We study how the toric code state changes to an IMTO state at the level of the averaged quantum trajectories. This phase transition is understood from the viewpoint of spontaneous symmetry breaking (SSB) of 1-form weak symmetry, that is, the IMTO is characterized by the symmetry restoration from the SSB, which comes from the proliferation of anyons. To understand the emergent IMTO, order and disorder parameters of 1-form symmetry are numerically studied by stabilizer simulation. The present study clarifies the existence of two distinct microscopic string operators for the fermionic anyons, that leads to distinct fermionic strong and weak 1-form symmetries, and also the obtained critical exponents indicate strong relation between IMTO and percolation.

arXiv comment14 pages, 6 figures, version to appear in Phys. Rev. B

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Cited by in corpus (5)

• Gauge theory and mixed state criticality
• Fundamental thresholds for computational and erasure errors via the coherent information
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits
• Noisy Monitored Quantum Circuits