Tensor network states are believed to describe gapped quantum phases faithfully. However, for critical states, a finite entanglement (cutoff) scaling has to be applied, for which the underlying theory is not clear yet. We propose a deformed conformal field theory (CFT) to understand the finite entanglement scaling in 1+1d. The finite entangled MPS states are determined by the corresponding CFT deformed a relevant perturbation. As a result, the bipartite entanglement Hamiltonian defined from the states can be understood as a boundary CFT with a physical and an entanglement boundary. The relevant operator, hence the physical conformal boundary and entanglement spectrum can be engineered by symmetries in MPS. Using critical lattice models, we illustrate the influence of the symmetry and the relevant deformation on conformal boundaries in the entanglement spectrum.

Rui-Zhen Huang is a BOF Postdoctoral Fellow working with Prof. Frank Verstraete at Ghent university since 2022. He obtained his Ph.D. from the Institute of Physics, Chinese Academy of Sciences in 2018 and continued his research in condensed matter theory as a postdoc at the University of Chinese Academy of Sciences.