Emergent Conformal Boundaries from Finite-Entanglement Scaling in Matrix Product States

Area of Science:

• Condensed Matter Physics
• Quantum Information Theory
• Statistical Mechanics

Background:

• Matrix product states (MPS) are vital for studying 1D critical lattice theories.
• Finite entanglement scaling is a key technique in these studies, particularly for systems with conformal symmetry.

Purpose of the Study:

• To investigate the role of finite entanglement as a relevant deformation in critical theories.
• To establish a connection between the entanglement Hamiltonian and boundary conformal field theory.
• To explore how MPS symmetries can engineer physical boundary conditions.

Main Methods:

• Utilizing finite entanglement scaling with matrix product states (MPS).
• Defining a bipartite entanglement Hamiltonian from MPS.
• Analyzing symmetry properties of MPS to engineer boundary conditions.
• Examining critical lattice models (Ising, Potts, free compact boson CFTs).

Main Results:

• Finite entanglement acts as a relevant deformation in 1D critical lattice theories.
• The entanglement Hamiltonian is shown to be a boundary conformal field theory.
• MPS symmetries allow for the engineering of physical conformal boundary conditions.
• The entanglement boundary is model-dependent and robust to the relevant perturbation.

Conclusions:

• Finite entanglement scaling provides a powerful framework for understanding boundary conformal field theory in lattice models.
• The interplay between MPS symmetries and relevant deformations dictates conformal boundary properties.
• This approach offers insights into the entanglement spectrum of critical systems.