  We study the properties of a spinless Hamiltonian which describes topological
nodal line semimetals at zero temperature. Our Hamiltonian has some resemblance
with the usual Hamiltonian for this type of materials, with that of Weyl
semimetals and is some sort of a generalisation of Kitaev Hamiltonian on
honeycomb lattice. As the interaction parameter of the Hamiltonian is varied,
it shows a transition from a gapless phase to a semimetal phase and then to
another semimetal phase. These transitions show up as non-analytic behaviour of
ground state energy. We find that one type of the semimetal is characterised by
a single closed loop of nodal line, while the other, by two such loops both
crossing the boundary of the first Brillouin zone. Surface states with non-zero
winding number are found to exist in both of these phases, but over two
topologically different regions. We also study the length of nodal line, the
area and perimeter of the region over which the winding number is non-zero and
the low-frequency electrical conductivity.
