RESUMO
We consider quantum many-body dynamics under quantum measurements, where the measurement-induced phase transitions (MIPs) occur when changing the frequency of the measurement. In this work, we consider the robustness of the MIP for long-range interaction that decays as r^{-α} with distance r. The effects of long-range interactions are classified into two regimes: (i) the MIP is observed (α>α_{c}), and (ii) the MIP is absent even for arbitrarily strong measurements (α<α_{c}). Using fermion models, we demonstrate both regimes in integrable and nonintegrable cases. We identify the underlying mechanism and propose sufficient conditions to observe the MIP, that is, α>d/2+1 for general bilinear systems and α>d+1 for general nonintegrable systems (d: spatial dimension). Numerical calculation indicates that these conditions are optimal.
