  In generic closed quantum systems, the complexity of operators increases
under time evolution governed by the Heisenberg equation, reflecting the
scrambling of local quantum information. However, when systems interact with an
external environment, the system-environment coupling allows operators to
escape from the system, inducing a dynamical transition between the scrambling
phase and the dissipative phase. This transition is known as the
environment-induced information scrambling transition, originally proposed in
Majorana fermion systems. In this work, we advance this dicovery by
investigating the transition in charge-conserved systems with space-time
randomness. We construct solvable Brownian Sachdev-Ye-Kitaev models of complex
fermions coupled to an environment, enabling the analytical computation of
operator growth. We determine the critical dissipation strength, which is
proportional to $n(1-n)$ with $n$ being the density of the complex fermions,
arising from the suppression in the quantum Lyapunov exponent due to the Pauli
blockade in the scattering process. We further analyze the density dependence
of maximally scrambled operators at late time. Our results shed light on the
intriguing interplay between information scrambling, dissipation, and
conservation laws.
