  We study entanglement renormalization group transformations for the ground
states of a spin model, called cubic code model $H_A$ in three dimensions, in
order to understand long-range entanglement structure. The cubic code model has
degenerate and locally indistinguishable ground states under periodic boundary
conditions. In the entanglement renormalization, one applies local unitary
transformations on a state, called disentangling transformations, after which
some of the spins are completely disentangled from the rest and then discarded.
We find a disentangling unitary to establish equivalence of the ground state of
$H_A$ on a lattice of lattice spacing $a$ to the tensor product of ground
spaces of two independent Hamiltonians $H_A$ and $H_B$ on lattices of lattice
spacing $2a$. We further find a disentangling unitary for the ground space of
$H_B$ with the lattice spacing $a$ to show that it decomposes into two copies
of itself on the lattice of the lattice spacing $2a$. The disentangling
transformations yield a tensor network description for the ground state of the
cubic code model. Using exact formulas for the degeneracy as a function of
system size, we show that the two Hamiltonians $H_A$ and $H_B$ represent
distinct phases of matter.
