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

Emergent conformal boundaries from finite-entanglement scaling in matrix product states