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Physics at the entangling surface · Around

2014

Physics at the entangling surface

Ohmori, Kantaro, Tachikawa, Yuji

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To consider the entanglement between the spatial region $A$ and its complement in a QFT, we need to assign a Hilbert space $\mathcal{H}_A$ to the region, by making a certain choice on the boundary $\partial A$.

We argue that a small physical boundary is implicitly inserted at the entangling surface.
We investigate these issues in the context of 2d CFTs, and show that we can indeed read off the Cardy states of the $c=1/2$ minimal model from the entanglement entropy of the critical Ising chain.

Built on

I. Affleck and A. W. W. Ludwig, “Universal Non-Integer ‘Groundstate Degeneracy’ in Critical Quantum Systems,” Phys.Rev.Lett
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C. Holzhey, F. Larsen, and F. Wilczek, “Geometric and renormalized entropy in conformal field theory,” Nucl.Phys
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P. Calabrese and J. L. Cardy, “Entanglement entropy and quantum field theory,” J.Stat.Mech
2004
Earlier work this paper cites.
J. Latorre, E. Rico, and G. Vidal, “Ground state entanglement in quantum spin chains,” Quant.Inf.Comput
2004
Earlier work this paper cites.

Similar

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J. Cardy and P. Calabrese, “Unusual Corrections to Scaling in Entanglement Entropy,” J.Stat.Mech
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Đ. Radičević, “Notes on Entanglement in Abelian Gauge Theories,” arXiv:1404.1391 [hep-th]
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D. Bianchini, O. A. Castro-Alvaredo, B. Doyon, E. Levi, and F. Ravanini, “Entanglement Entropy of Non Unitary Conformal Field Theory,” arXiv:1405.2804 [hep-th]
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Cited in the paper.

Then

P. Calabrese, J. Cardy, and I. Peschel, “Corrections to scaling for block entanglement in massive spin chains,” J.Stat.Mech
Original
2010
Later among the works it cites.
W. Donnelly, “Decomposition of entanglement entropy in lattice gauge theory,” Phys.Rev
Original
2012
Later among the works it cites.
P. Deift, A. Its, and I. Krasovsky, “Toeplitz matrices and toeplitz determinants under the impetus of the ising model: Some history and some recent results,” Communications on Pure and Applied Mathematics
Original
2013
Later among the works it cites.
H. Casini, M. Huerta, and J. A. Rosabal, “Remarks on entanglement entropy for gauge fields,” Phys.Rev
Original
2014
Closest in time.

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