  The critical theories for the topological phase transitions of integer
quantum Hall states to a trivial insulating state with the same symmetry can be
obtained by calculating the ground state entanglement spectrum under a
symmetric checkerboard bipartition. In contrast to the gapless edge excitations
under the left-right bipartition, a quantum network with bulk gapless
excitations naturally emerges at the Brillouin zone center without fine tuning.
On a large finite lattice, the resulting critical theory for the $\nu =1$ state
is the (2+1) dimensional relativistic quantum field theory characterized by a
\textit{single} Dirac cone spectrum and a pair of \textit{fractionalized}
zero-energy states, while for the $\nu =2$ state the critical theory exhibits a
parabolic spectrum and no sign of fractionalization in the zero-energy states.
A triangular correspondence is established among the bulk topological theory,
gapless edge theory, and the critical theory via the ground state entanglement
spectrum.
