Boundary dissipation in Ising CFT

Boundary conformal field theory (CFT) is one of few exact analytical tools for the study of quantum non-equilibrium systems, yet so far has been primarily restricted to closed Hamiltonian systems. We study one of the simplest CFTs, namely thequantum critical Ising model with boundary dephasing along the direction of the most relevant boundary operator. Naïve scaling arguments suggest that such dissipation should be marginal. Numerically for large systems, we find that boundary spin in the presence of dissipation, with or without boundary field, depolarizes and reaches a nonequilibrium steady state (NESS). In the presence of RG-relevant boundary term, scaling functions appear unmodified, suggesting that the dissipation is marginally irrelevant in that case. In the absence of boundary field, we study modifications of the Zeno effect by Keldysh RG and numerical calculations of the two-time correlation function of the boundary spin. Finally, we comment on potential application to other CFTs