Regensburg 2016 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 63: Low-Dimensional Systems: 2D - Theory

TT 63.7: Talk

Thursday, March 10, 2016, 11:00–11:15, H21

Boson-fermion duality for corner entanglement entropies in free field theories — •Johannes Helmes^1,2, Lauren Hayward Sierens^2,3, Anushya Chandran², and Roger Melko^2,3 — ¹University of Cologne, Germany — ²Perimeter Institute, Waterloo, Canada — ³University of Waterloo, Canada

Subleading corrections to the prevalent area-law of (Rényi) entanglement entropies of critical quantum many-body systems are known to show universal behavior. For gapless systems a logarithmic correction arises from the presence of corners in the subsystem. Its coefficient is concretely related to the central charge of the stress tensor of the low-energy effective conformal field theory (CFT) and hence counts the underlying degrees of freedom. A surprising duality is revealed in these corner terms of an opening angle θ ≲ π between free boson and Dirac fermion lattice field theories for reciprocal Rényi indices.

We compute the entanglement entropies via an exact lattice diagonalization supplemented by a numerical linked-cluster expansion. Using these data we show that the duality is also relatively robust for a corner with an opening angle of θ = π /2. We furthermore apply our numerical treatment to a variety of other angles θ. The results confirm the scaling of the corner term with ( θ − π)² and shed light on the gradual dissolution of the duality in the limit of small angles.