Quantum Zeno transition in boundary-dissipative Ising model

The one-dimensional Ising model plays a defining role in many-body physics as one of few solvable models of quantum criticality. We study the one-dimensional Ising model in the presence of boundary dissipation. Numerically we find that in the presence of boundary dissipation boundary spin reaches a nonequilibrium steady state, which from naïve scaling arguments and RG calculation suggest that such dissipation is marginal. From our calculations of two-time correlation of the boundary spin, we find that the dynamics are singular near the Ising critical point, as well as showing new critical behavior at large dissipation. From TEBD calculations, we find these singularities to be robust to interactions. Analytically, our system can be mapped to a two-legged non-Hermitian model and we find that it has a singular edge spectrum with sharp transitions between 0, 1, and 2 edge states.