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

Abstract

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.

6+7 pages,4+7 figures; add nn RVB iPEPS result

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• Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Probing universal critical scaling with scan-DMRG
• Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model
• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality
• Chiral Edge States Emerging on Anyon-Net
• Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling
• Universal entanglement correction induced by relevant deformations at the quantum critical point
• Entanglement scaling and criticality of infinite-size quantum many-body systems in continuous space addressed by a tensor network approach