  We consider a one-dimensional Dicke lattice with complex photon hopping
amplitudes and investigate the influence of time-reversal symmetry breaking due
to synthetic magnetic fields. We show that, by tuning the total flux threading
the lattice with a periodic boundary condition, the universality class of
superradiant phase transition (SPT) changes from that of the mean-field fully
connected systems to one that features anomalous critical phenomena. The
anomalous SPT exhibits a closing of the energy gap with different critical
exponents on both sides of transition and a discontinuity of correlations and
fluctuation despite it being a second-order phase transition. In the anomalous
normal phase, we find that a non-mean-field critical exponent for the closing
energy gap and nondivergent fluctuations and correlations appear, which we
attribute to the asymmetric dispersion relation. Moreover, we show that the
nearest neighborhood complex hopping induces effective long-range interactions
for position quadratures of the cavity fields, whose competition leads to a
series of first-order phase transitions among superradiant phases with varying
degrees of frustration. The resulting multicritical points also show anomalous
features such as two coexisting critical scalings on both sides of the
transition. Our work shows that the interplay between the broken time-reversal
symmetry and frustration on bosonic lattice systems can give rise to anomalous
critical phenomena that have no counterpart in fermionic, spin, or
time-reversal symmetric quantum optical systems.
