  The competition between scrambling unitary evolution and projective
measurements leads to a phase transition in the dynamics of quantum
entanglement. Here, we demonstrate that the nature of this transition is
fundamentally altered by the presence of long-range, power-law interactions.
For sufficiently weak power-laws, the measurement-induced transition is
described by conformal field theory, analogous to short-range-interacting
hybrid circuits. However, beyond a critical power-law, we demonstrate that
long-range interactions give rise to a continuum of non-conformal universality
classes, with continuously varying critical exponents. We numerically determine
the phase diagram for a one-dimensional, long-range-interacting hybrid circuit
model as a function of the power-law exponent and the measurement rate.
Finally, by using an analytic mapping to a long-range quantum Ising model, we
provide a theoretical understanding for the critical power-law.
