Measurement-only dynamics in the one-dimensional XY model

Intriguing critical dynamics can appear by using frustrated measurements on a quantum state. For instance, performing random ZZ and X measurements on a 1D spin chain can induce a symmetry-breaking-like phase transition but with a different type of universality class. In this presentation, we discuss a measurement-only analog of the 1D XY model, in which nearest-neighbor XX and YY measurements are performed with probabilities p and 1-p respectively. By performing a Jordan-Wigner transformation, we show that this model leads to two decoupled Majorana wires with free-fermion dynamics. The critical point has an emergent U(1) spin rotational symmetry. We further perturb this model by including single-site Z measurements, which map to local inter-wire couplings in the bipartite system. The phase diagram and the scaling of mutual information and negativity are generated numerically, and connections to classical loop models are discussed.