# Physical meaning of constant zero phonon dispersion relation

Consider a 2D lattice model like this

Assuming the mass of atom and force constant is 1, we could easily calculate the dispersion relations of the system. As there are four atoms per unit cell, there should be eight eigenvalues for every wave-vector $$k$$. The dispersion relation is like below We see that there are two zero energy bands or constant zero dispersion relations in the figure, now my question is:

What is the physical meaning or how to understand the zero energy bands?