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

• URL: http://arxiv.org/abs/2306.08163v2
• Date: Tue, 27 Feb 2024 21:18:23 GMT
• Title: Emergent conformal boundaries from finite-entanglement scaling in matrix product states
• Authors: Rui-Zhen Huang, Long Zhang, Andreas M. L\"auchli, Jutho Haegeman, Frank Verstraete, and Laurens Vanderstraeten
• Abstract summary: We argue that finite entanglement introduces a relevant deformation in the critical theory. We exploit the symmetry properties of the MPS to engineer the physical conformal boundary condition. 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.
• Score: 2.2830210220010256
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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