  First, we study a square fermionic lattice that supports the existence of
massless Dirac fermions, where the Dirac points are protected by a hidden
symmetry. We also consider two modified models with a staggered potential and
the diagonal hopping terms, respectively. In the modified model with a
staggered potential, the Dirac points exist in some range of magnitude of the
staggered potential, and move with the variation of the staggered potential.
When the magnitude of the staggered potential reaches a critical value, the two
Dirac points merge. In the modified model with the diagonal hopping terms, the
Dirac points always exist and just move with the variation of amplitude of the
diagonal hopping. We develop a mapping method to find hidden symmetries
evolving with the parameters. In the two modified models, the Dirac points are
protected by this kind of hidden symmetry, and their moving and merging process
can be explained by the evolution of the hidden symmetry along with the
variation of the corresponding parameter.
