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 $r^{-α}$ 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 non-integrable 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 non-integrable systems ($d$: spatial dimension). Numerical calculation indicates that these conditions are optimal.

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