On the entanglement across a cubic interface in 3+1 dimensions

Abstract

We calculate the area, edge and corner Renyi entanglement entropies in the ground state of the transverse-field Ising model, on a simple-cubic lattice, by high-field and low-field series expansions. We find that while the area term is positive and the line term is negative as required by strong subadditivity, the corner contributions are positive in 3-dimensions. Analysis of the series suggests that the expansions converge up to the physical critical point from both sides. The leading area-law Renyi entropies match nicely from the high and low field expansions at the critical point, forming a sharp cusp there. We calculate the coefficients of the logarithmic divergence associated with the corner entropy and compare them with conformal field theory results with smooth interfaces and find a striking correspondence.

arXiv comment5 pages, 6 figures

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• Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
• Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice
• Entanglement entropies of the $J_1-J_2$ Heisenberg antiferromagnet on the square lattice
• Generalizing the entanglement entropy of singular regions in conformal field theories
• Relating bulk to boundary entanglement
• Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points
• Entanglement susceptibilities and universal geometric entanglement entropy
• Cubic trihedral corner entanglement for a free scalar
• Probing trihedral corner entanglement for Dirac fermions
• Universal divergence of the Renyi entropy of a thinly sliced torus at the Ising fixed point