  Landau's spontaneous symmetry breaking theory is a fundamental theory that
describes the collective behaviors in many-body systems. It was well known that
for usual spontaneous symmetry breaking in Hermitian systems, the
order-disorder phase transition with gap closing and spontaneous symmetry
breaking occur at the same critical point. In this paper, we generalized the
Landau's spontaneous symmetry breaking theory to the cases in non-Hermitian
(NH) many-body systems with biorthogonal Z2 symmetry and tried to discover
certain universal features. We were surprised to find that the effect of the NH
terms splits the spontaneous biorthogonal Z2 symmetry breaking from a
(biorthogonal) order-disorder phase transition with gap closing. The sudden
change of similarity for two degenerate ground states indicates a new type of
quantum phase transition without gap closing accompanied by spontaneous
biorthogonal Z2 symmetry breaking. We will take the NH transverse Ising model
as an example to investigate the anomalous spontaneous symmetry breaking. The
numerical results were consistent with the theoretical predictions.
