  Effective relativistic field theory models capable of realizing various
gapless topological states are presented in this work. We study the topological
phase transitions of the Weyl and nodal line semimetal states in effective
field theories. When the one form field giving rise to the Weyl nodes lie
perpendicular to the plane where the nodal ring lives, the nodal ring and Weyl
nodes could coexist as the mirror symmetry responsible for the nodal ring is
not broken. New phases including a three-node state and a triple degenerate
state exist. The nodal ring is immediately destroyed when the one form field
lies in the plane of the ring. However, we show that in an eight-component
spinor model, Weyl nodes and nodal rings could still coexist even when the one
form field is parallel to the plane, due to the expanded symmetry. Topological
invariants are calculated which confirm the interesting nontrivial topology of
the three-node state and the triple-degenerate node. This work presents
potential topological phase transitions in multiphase topological systems,
which may be experimentally detected.
