  The order from quantum disorders (OFQD) phenomenon is well-known and
ubiquitous in particle physics and frustrated magnetic systems. Typically, OFQD
transfers a spurious Goldstone mode into a pseudo-Goldstone mode with a tiny
gap. Here, we report an opposite phenomenon: OFQD transfers a spurious
quadratic mode into a true linear Goldstone mode with a very small velocity
(named slow-Goldstone mode). This new phenomenon is demonstrated in an
interacting bosonic system subjected to an Abelian flux. We develop a new and
systematic OFQD analysis to determine the true quantum ground state and the
whole excitation spectrum. In the weak-coupling limit, the superfluid ground
state has a 4-sublattice 90? coplanar spin structure, which supports 4 linear
Goldstone modes with 3 different velocities. One of which is generated by the
OFQD is much softer than the other 3 Goldstone modes, so it can be easily
detected in the cold atom or photonic experiments. In the strong-coupling
limit, the ferromagnetic Mott ground state with a true quadratic Goldstone
mode. We speculate that there could be some topological phases intervening
between the two symmetry broken states. These novel phenomena may be observed
in the current cold-atom or photonic experiments subjected to an Abelian flux
at the weak coupling limit where the heatings may be well under control.
Possible connections to Coleman-Weinberg potential in particle physics, 1/N
expansion of Sachdev-Ye-Kitaev models, and zero temperature quantum black hole
entropy are outlined.
