  We show that the entire continuous model of twisted bilayer graphene (TBG)
(and not just the two active bands) with particle-hole symmetry is anomalous
and hence incompatible with a lattice model. Previous works, e.g., [Phys. Rev.
Lett. 123, 036401], [Phys. Rev. X 9, 021013], [Phys. Rev. B 99, 195455], and
others [1-4] found that the two flat bands in TBG possess a fragile topology
protected by the $C_{2z}T$ symmetry. [Phys. Rev. Lett. 123, 036401] also
pointed out an approximate particle-hole symmetry ($\mathcal{P}$) in the
continuous model of TBG. In this work, we numerically confirm that
$\mathcal{P}$ is indeed a good approximation for TBG and show that the fragile
topology of the two flat bands is enhanced to a $\mathcal{P}$-protected stable
topology. This stable topology implies $4l+2$ ($l\in\mathbb{N}$) Dirac points
between the middle two bands. The $\mathcal{P}$-protected stable topology is
robust against arbitrary gap closings between the middle two bands the other
bands. We further show that, remarkably, this $\mathcal{P}$-protected stable
topology, as well as the corresponding $4l + 2$ Dirac points, cannot be
realized in lattice models that preserve both $C_{2z}T$ and $\mathcal{P}$
symmetries. In other words, the continuous model of TBG is anomalous and cannot
be realized on lattices. Two other topology related topics, with consequences
for the interacting TBG problem, i.e., the choice of Chern band basis in the
two flat bands and the perfect metal phase of TBG in the so-called second
chiral limit, are also discussed.
