Publication: Entanglement scaling in two-dimensional gapless systems

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Title Entanglement scaling in two-dimensional gapless systems
Authors/Editors* H Ju, AB Kallin, P Fendley, MB Hastings, RG Melko
Where published* Physical Review B
How published* Journal
Year* 2012
Volume 85
Number 16
Pages 165121
We numerically determine subleading scaling terms in the ground-state entanglement entropy of several two-dimensional (2D) gapless systems, including a Heisenberg model with Néel order, a free Dirac fermion in the π-flux phase, and the nearest-neighbor resonating-valence-bond wave function. For these models, we show that the entanglement entropy between cylindrical regions of length x and L−x, extending around a torus of length L, depends on the dimensionless ratio x/L. This can be well approximated on finite-size lattices by a function ln(sin(πx/L)), akin to the familiar chord-length dependence in one dimension. We provide evidence, however, that the precise form of this bulk-dependent contribution is a more general function in the 2D thermodynamic limit.

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