Zeno effect of the open quantum system in the presence of 1/f noise

We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in a two-level system(TLS) interacting with an environment owning 1/f noise. Using a numerically exact method based on the thermo field dynamics(TFD) theory and the matrix product states(MPS), we obtain exact evolutions of the TLS and bath(environment) under repetitive measurements at both zero and finite temperatures. At zero temperature, we observe a novel transition from a pure QZE in the short time scale to a QZE-QAZE crossover in the long time scale, by considering the measurement induced non-Markvoian effect. At finite temperature, we exploit that the thermal fluctuation suppresses the decay of the survival probability in the short time scale, whereas it enhances the decay in the long time scale.