Corner entanglement scaling with projected entangled pair states

Quantum entanglement serves as a vital tool for characterizing strongly correlated many-body systems, particularly in identifying universal properties at quantum critical points. While the leading term of the entanglement entropy in two dimensions follows an area law, the subleading logarithmic contribution—specifically when the bipartition includes a corner—encodes universal information about the underlying conformal field theory (CFT). This paper introduces a robust numerical method to compute this corner entanglement entropy directly in the thermodynamic limit using projected entangled pair states (PEPS).

The authors utilize the bulk-boundary correspondence to construct an effective entanglement Hamiltonian for a corner-shaped bipartition. By representing the ground state as an infinite PEPS, they optimize the tensor network variationally and compute the boundary matrix product states (MPS) for both linear and corner geometries. The corner contribution is isolated by subtracting the area law component, allowing for the study of its scaling behavior relative to the effective correlation length induced by the finite bond dimension of the boundary MPS.

The researchers validated their method by applying it to the 2D transverse field Ising model and the bilayer XY model at their respective critical points. In both cases, they observed the expected logarithmic scaling of the corner contribution with the correlation length. The extracted corner coefficients are consistent with existing literature from quantum Monte Carlo and series expansion methods. Furthermore, the authors demonstrated that for a gapped chiral spin liquid, the corner contribution converges to a finite value rather than scaling logarithmically, confirming the method's ability to distinguish between critical and gapped phases.