  The use of finite entanglement scaling with matrix product states (MPS) has
become a crucial tool for studying 1+1d critical lattice theories, especially
those with emergent conformal symmetry. We argue that finite entanglement
introduces a relevant deformation in the critical theory. As a result, the
bipartite entanglement Hamiltonian defined from the MPS can be understood as a
boundary conformal field theory with a physical and an entanglement boundary.
We are able to exploit the symmetry properties of the MPS to engineer the
physical conformal boundary condition. The entanglement boundary, on the other
hand, is related to the concrete lattice model and remains invariant under this
relevant perturbation. Using critical lattice models described by the Ising,
Potts, and free compact boson CFTs, we illustrate the influence of the symmetry
and the relevant deformation on the conformal boundaries in the entanglement
spectrum.
