  This study delves into the concept of quantum phases in open quantum systems,
examining the shortcomings of existing approaches that focus on steady states
of Lindbladians and highlighting their limitations in capturing key phase
transitions. In contrast to these methods, we introduce the concept of
imaginary-time Lindbladian evolution as an alternative framework. This new
approach defines gapped quantum phases in open systems through the spectrum
properties of the imaginary-Liouville superoperator. We find that, in addition
to all pure gapped ground states, the Gibbs state of a stabilizer Hamiltonian
at any finite temperature can also be characterized by our scheme, demonstrated
through explicit construction. To illustrate the effectiveness of this
framework, we apply it to investigate the phase diagram for open systems with
$\mathbb{Z}_{2}^{\sigma} \times \mathbb{Z}_{2}^{\tau}$ symmetry, including
cases with nontrivial average symmetry protected topological order or
spontaneous symmetry breaking order. Our findings demonstrate universal
properties at quantum criticality, such as nonanalytic behaviors of
steady-state observables, divergence of correlation lengths, and closing of the
imaginary-Liouville gap. These results advance our understanding of quantum
phase transitions in open quantum systems.
