  Understanding phases of matter is of both fundamental and practical
importance. Prior to the widespread appreciation and acceptance of topological
order, the paradigm of spontaneous symmetry breaking, formulated along the
Landau-Ginzburg-Wilson (LGW) dogma, is central to understanding phases
associated with order parameters of distinct symmetries and transitions between
phases. This work proposes to identify ground state phases of quantum many-body
system in terms of time order, which is operationally defined by the appearance
of nontrivial temporal structure in the two-time auto-correlation function of a
symmetry operator (order parameter). As a special case, the (symmetry
protected) time crystalline order phase detects continuous time crystal (CTC).
Time order phase diagrams for spin-1 atomic Bose-Einstein condensate (BEC) and
quantum Rabi model are fully worked out. Besides time crystalline order, the
intriguing phase of time functional order is discussed in two non-Hermitian
interacting spin models.
