Noisy Effects in Integrable Quantum Circuits with Boundary Defects

We conduct a theoretical investigation into the dynamics of open quantum systems, specifically examining integrable quantum circuits in the Trotterized limit under the influence of onsite dephasing noise, featuring a spin-1/2 "impurity" located at the edge. By using a combination of Bethe Ansatz (BA) and exact diagonalization (ED), we analyze the dynamics of both the bulk system and the impurity within the contexts of the XXX (Heisenberg) and XX qubit chains, considering scenarios both with and without bulk noise. In the absence of noise, our findings reveal that the impurity can exist in two distinct phases: the bound mode phase, characterized by persistent oscillations of impurity magnetization over time, and the Kondo phase, marked by screening of the impurity on a timescale associated with the Kondo effect. Upon introducing bulk dephasing noise, we observe that in the long-time limit, the dynamics of the impurity magnetization exhibit a quantum Zeno effect, where increased noise strength γ results in a slowdown of the impurity's dynamics. Notably, in the bound mode regime, the impurity magnetization decays more rapidly with increasing noise strength at shorter timescales. We attribute the Zeno effect, which impedes the impurity's dynamics in the long-time limit, due to the diffusive behavior of the bulk transport in the presence of noise.