Decoherence-induced self-dual criticality in topological states of matter (2502.14034v3)

Abstract: Quantum measurements can be employed to induce decoherence in a restricted segment of a larger quantum many-body state, while generating entanglement for its remaining constituents. We demonstrate generally that measurement-induced phase transitions can be viewed as decoherence-induced critical mixed states. In this context, a deeper conceptual understanding is called for with regard to symmetry as an organizing principle. Integrating these connections we investigate the role of self-dual symmetry in mixed states, showing that the decoherence of electric (e) and magnetic (m) vortices from the 2D bulk of the toric code, or equivalently, a 2D cluster state with symmetry-protected topological order, can leave a (1+1)D quantum critical mixed state on the boundary protected by a weak Kramers-Wannier self-dual symmetry. The corresponding self-dual critical bulk is described by the $N\to1$ limit of the 2D Non-linear Sigma Model in symmetry class D with target space SO(2N)/U(N) at $\Theta$-angle $\pi$, and represents a "measurement-version" of the Cho-Fisher network model subjected to Born-rule randomness. Explicit breaking of self-duality, by incoherent noise amounting to fermion interactions or (non-interacting) coherent deformation, is shown to induce an RG crossover from this self-dual critical state to Nishimori criticality or to it from a novel type of Ising+ criticality, respectively, both related to the random-bond Ising model in different replica limits. Using an unbiased numerical approach combining tensor network, Monte Carlo, and Gaussian fermion simulations, we chart out a global phase diagram as diagnosed by coherent information and entanglement entropy measures. Our results point to a way towards a general understanding of mixed-state criticality in open quantum systems in terms of symmetry and topology.