  Conformal Field Theories (CFTs) have been used extensively to understand the
physics of critical lattice models at equilibrium. However, the applicability
of CFT calculations to the behavior of the lattice systems in the
out-of-equilibrium setting is not entirely understood. In this work, we compare
the CFT results of the evolution of the entanglement spectrum after a quantum
quench with numerical calculations of the entanglement spectrum of the
three-state Potts model using matrix product state simulations. Our results
lead us to conjecture that CFT does not describe the entanglement spectrum of
the three-state Potts model at long times, contrary to what happens in the
Ising model. We thus numerically simulate the out-of-equilibrium behaviour of
the Potts model according to the CFT protocol - i.e. by taking a particular
product state and "cooling" it, then quenching to the critical point and find
that, in this case, the entanglement spectrum is indeed described by the CFT at
long times.
