Fate of measurement-induced phase transition in long-range interactions

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 $r^{-\alpha}$ with distance $r$. The effects of long-range interactions are classified into two regimes: (i) the MIP is observed $(\alpha > \alpha_c)$, and (ii) the MIP is absent even for arbitrarily strong measurements $(\alpha<\alpha_c)$. Using fermion models, we demonstrate both regimes in integrable and non-integrable cases. We identify the underlying mechanism and propose sufficient conditions to observe the MIP, that is, $\alpha > d/2+1$ for general bilinear systems and $\alpha > d+1$ for general non-integrable systems ($d$: spatial dimension). Numerical calculation indicates that these conditions are optimal.