  We study an improved holographic model for the strongly coupled nodal line
semimetal which satisfies the duality relation between the rank two tensor
operators $\bar{\psi}\gamma^{\mu \nu}\psi$ and $\bar{\psi}\gamma^{\mu
\nu}\gamma^5\psi$. We introduce a Chern-Simons term and a mass term in the bulk
for a complex two form field which is dual to the above tensor operators and
the duality relation is automatically satisfied from holography. We find that
there exists a quantum phase transition from a topological nodal line semimetal
phase to a trivial phase. In the topological phase, there exist multiple nodal
lines in the fermionic spectrum which are topologically nontrivial. The bulk
geometries are different from the previous model without the duality
constraint, while the resulting properties are qualitatively similar to those
in that model. This improved model provides a more natural ground to analyze
transports or other properties of strongly coupled nodal line semimetals.
