  The paradigm of second-order phase transition and symmetry breaking for
thermal and quantum systems is a pillar of modern physics that has been
fruitfully applied to out-of-equilibrium open quantum systems. Despite the
non-equilibrium nature of lasing, the laser threshold was compared with thermal
phase transitions systems more than forty years ago. For instance, the Landau
theory -- based on thermodynamical consideration -- has been used to
characterize the Scully-Lamb laser model (SLLM), describing a single-mode laser
without saturable absorbers. Accordingly, the laser threshold is a second-order
phase transition, associated with a spontaneous symmetry breaking (SSB) of the
$U(1)$ symmetry of the model. To capture a genuine non-equilibrium, quantum,
and dissipative phase transition of the SLLM, here we employ a Liouvillian
superoperator formalism derived from a Lindblad master equation. Our results
confirm that the $U(1)$ SSB can occur at the lasing threshold but, in contrast
to the Landau theory and semiclassical approximation, they signal that the SLLM
"fundamental" transition is a different phenomenon, which we call Liouvillian
spectral collapse; that is, the emergence of diabolic points of infinite
degeneracy. By considering a generalized SLLM with additional dephasing, we
witness a second-order phase transition, with a Liouvillian spectral collapse,
but in the absence of symmetry breaking. This demonstrates the difference
between the Liouvillian spectral collapse and a standard second-order phase
transition with symmetry breaking. We characterize the new phenomena associated
with the spectral collapse, such as the onset of a rather unusual
multistability enabled (and not suppressed) by the very presence of
fluctuations. This multistability, characterizing the dissipative and quantum
origin of lasing, can be experimentally revealed by the presence of a dynamical
hysteresis.
