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We explore the dynamical phases of unitary Clifford circuits withvariable-range interactions, coupled to a monitoring environment. Weinvestigate two classes of models, distinguished by the action of the unitarygates, which either are organized in clusters of finite-range two-body gates,or are pair-wise interactions randomly distributed throughout the system with apower-law distribution. We find the range of the interactions plays a key rolein characterizing both phases and their measurement-induced transitions. Forthe cluster unitary gates we find a transition between a phase with volume-lawscaling of the entanglement entropy and a phase with area-law entanglemententropy. Our results indicate that the universality class of the phasetransition is compatible to that of short range hybrid Clifford circuits.Oppositely, in the case of power-law distributed gates, we find theuniversality class of the phase transition changes continuously with theparameter controlling the range of interactions. In particular, forintermediate values of the control parameter, we find a non-conformal criticalline which separates a phase with volume-law scaling of the entanglemententropy from one with sub-extensive scaling. Within this region, we find theentanglement entropy and the logarithmic negativity present a cross-over from aphase with algebraic growth of entanglement with system size, and an area-lawphase.

Measurement-induced criticality in extended and long-range unitary circuits