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

TL;DR

This paper explores how finite entanglement scaling in matrix product states reveals emergent conformal boundaries in 1+1d critical theories, linking boundary conditions to symmetry and relevant deformations.

Contribution

It demonstrates that finite entanglement acts as a relevant deformation, allowing the engineering of physical conformal boundaries via MPS symmetry properties.

Findings

Finite entanglement introduces a relevant deformation in critical theories.

The bipartite entanglement Hamiltonian acts as a boundary conformal field theory.

Symmetry properties of MPS can be used to engineer physical boundary conditions.

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.