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Cited by 230

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Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

Faulkner, Thomas, Leigh, Robert G., Parrikar, Onkar, Wang, Huajia·2016·Journal of High Energy Physics
DOI 10.1007/jhep09(2016)038
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Figures

Figure 1 We deform the half space A 0 (solid blue line) inwards into the region A (solid red line), such that D ( A ) (darker shaded region) is contained inside D ( A 0 ) (lighter shaded region). Also shown are the Rindler horizons H ± corresponding to the regions A 0 and A c 0 . (The transverse directions ⃗ x are implicit.)
Figure 1 We deform the half space A 0 (solid blue line) inwards into the region A (solid red line), such that D ( A ) (darker shaded region) is contained inside D ( A 0 ) (lighter shaded region). Also shown are the Rindler horizons H ± corresponding to the regions A 0 and A c 0 . (The transverse directions ⃗ x are implicit.)CC-BY · From the PDF
Figure 2 The path integral construction for matrix elements of the reduced density matrix for the state | ψ α 〉 , over the original half space A 0 (solid blue line). The operator insertions are marked at x 0 E = ± τ . The black dot is the entangling surface (with transverse directions ⃗ x implicit).
Figure 2 The path integral construction for matrix elements of the reduced density matrix for the state | ψ α 〉 , over the original half space A 0 (solid blue line). The operator insertions are marked at x 0 E = ± τ . The black dot is the entangling surface (with transverse directions ⃗ x implicit).CC-BY · From the PDF
Figure 3 We split the region of integration into two parts: the region inside the dotted line is R b , and the region outside is ˜ R . Also shown is the brach-cut ∂ ˜ R ± .
Figure 3 We split the region of integration into two parts: the region inside the dotted line is R b , and the region outside is ˜ R . Also shown is the brach-cut ∂ ˜ R ± .CC-BY · From the PDF
Figure 4 The contribution from inside the region R b can be written in real time as an integral over the shaded region.
Figure 4 The contribution from inside the region R b can be written in real time as an integral over the shaded region.CC-BY · From the PDF
Figure 5 The path integral construction of the regulated reduced density matrix for an excited state. We cut out a cylindrical region of radius r = a around the entangling surface, with brickwall-like boundary conditions. Also shown is the fictitious cutoff surface of radius r = b .
Figure 5 The path integral construction of the regulated reduced density matrix for an excited state. We cut out a cylindrical region of radius r = a around the entangling surface, with brickwall-like boundary conditions. Also shown is the fictitious cutoff surface of radius r = b .CC-BY · From the PDF

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Metadata

Authors
Faulkner, T., Leigh, R. G., Parrikar, O., & Wang, H.
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2016-09
Volume
2016
Issue
9
ISSN
1029-8479
DOI
10.1007/jhep09(2016)038
Cited by
230
References
13
Language
en

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Faulkner, T., Leigh, R. G., Parrikar, O., & Wang, H. (2016). Modular Hamiltonians for deformed half-spaces and the averaged null energy condition. Journal of High Energy Physics. https://doi.org/10.1007/jhep09(2016)038

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