Built on

J. L. Cardy, “Boundary Conditions, Fusion Rules and the Verlinde Formula,” Nucl. Phys. B 324
1989
Earlier work this paper cites.
N. Ishibashi, “The Boundary and Crosscap States in Conformal Field Theories,” Mod. Phys. Lett. A 4
1989
Earlier work this paper cites.
I. Affleck and A. W. W. Ludwig, “Universal noninteger ’ground state degeneracy’ in critical quantum systems,” Phys. Rev. Lett. 67
1991
Earlier work this paper cites.
C. Holzhey, F. Larsen and F. Wilczek, “Geometric and renormalized entropy in conformal field theory,” Nucl. Phys. B 424
1994
Earlier work this paper cites.
G. ’t Hooft, “Dimensional reduction in quantum gravity,” [arXiv:gr-qc/9310026]; L. Susskind, “The World as a hologram,” J. Math. Phys. 36
1995
Earlier work this paper cites.
J. M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2
1999
Earlier work this paper cites.
P. Calabrese and J. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech. 0406
2004
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, “Evolution of Entanglement Entropy in One-Dimensional Systems,” J. Stat. Mech. 04
2005
Earlier work this paper cites.
S. Ryu and Y. Hatsugai, “Entanglement entropy and the Berry phase in the solid state,” Phys. Rev. B 73
2006
Earlier work this paper cites.

Similar

G. Vidal,“Entanglement renormalization,” Phys. Rev. Lett. 99
Original
2007
Cited alongside, same era.
A. Kitaev, “Periodic table for topological insulators and superconductors,” AIP Conf. Proc. 1134
2009
Cited alongside, same era.
J. I. Cirac and F. Verstraete, “Renormalization and tensor product states in spin chains and lattices,” J. Phys. A: Math. Theor. 42
Original
2009
Cited alongside, same era.
M. Van Raamsdonk, “Comments on quantum gravity and entanglement,” arXiv:0907.2939 [hep-th]; “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42
Original
2010
Cited alongside, same era.
T. Takayanagi and T. Ugajin, “Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining,” JHEP 1011
Original

Then

M. Z. Hasan and C. L. Kane, ”Colloquium: Topological insulators,” Rev. Mod. Phys. 82
Original
2011
Later among the works it cites.
I. Heemskerk and J. Polchinski, “Holographic and Wilsonian Renormalization Groups,” JHEP 1106
Original
2011
Later among the works it cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
Original
2012
Later among the works it cites.
B. Swingle, “Entanglement Renormalization and Holography,” Phys. Rev. D 86
Original
2012
Later among the works it cites.
M. Nozaki, S. Ryu and T. Takayanagi, “Holographic Geometry of Entanglement Renormalization in Quantum Field Theories,” JHEP 1210
Original

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2014

Boundary States as Holographic Duals of Trivial Spacetimes

Miyaji, Masamichi, Ryu, Shinsei, Takayanagi, Tadashi et al.

Understand

We study real-space quantum entanglement included in conformally invariant boundary states in conformal field theories (CFTs).

First, we argue that boundary states essentially have no real-space entanglement by computing the entanglement entropy when we bipartite the system into two spatial regions.
From the viewpoint of holography, this shows that boundary states are dual to trivial spacetimes of zero spactime volume.
Next, we point out that a continuous multiscale entanglement renormalization ansatz (cMERA) for any CFTs can be formulated by employing a boundary state as its infrared unentangled state with an appropriate regularization.

Built on

J. L. Cardy, “Boundary Conditions, Fusion Rules and the Verlinde Formula,” Nucl. Phys. B 324
1989
Earlier work this paper cites.
N. Ishibashi, “The Boundary and Crosscap States in Conformal Field Theories,” Mod. Phys. Lett. A 4
1989
Earlier work this paper cites.
I. Affleck and A. W. W. Ludwig, “Universal noninteger ’ground state degeneracy’ in critical quantum systems,” Phys. Rev. Lett. 67
1991
Earlier work this paper cites.
C. Holzhey, F. Larsen and F. Wilczek, “Geometric and renormalized entropy in conformal field theory,” Nucl. Phys. B 424
1994
Earlier work this paper cites.
G. ’t Hooft, “Dimensional reduction in quantum gravity,” [arXiv:gr-qc/9310026]; L. Susskind, “The World as a hologram,” J. Math. Phys. 36
1995
Earlier work this paper cites.
J. M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2
1999
Earlier work this paper cites.
P. Calabrese and J. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech. 0406
2004
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, “Evolution of Entanglement Entropy in One-Dimensional Systems,” J. Stat. Mech. 04
2005
Earlier work this paper cites.
S. Ryu and Y. Hatsugai, “Entanglement entropy and the Berry phase in the solid state,” Phys. Rev. B 73
2006
Earlier work this paper cites.

Similar

G. Vidal,“Entanglement renormalization,” Phys. Rev. Lett. 99
Original
2007
Cited alongside, same era.
A. Kitaev, “Periodic table for topological insulators and superconductors,” AIP Conf. Proc. 1134
2009
Cited alongside, same era.
J. I. Cirac and F. Verstraete, “Renormalization and tensor product states in spin chains and lattices,” J. Phys. A: Math. Theor. 42
Original
2009
Cited alongside, same era.
M. Van Raamsdonk, “Comments on quantum gravity and entanglement,” arXiv:0907.2939 [hep-th]; “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42
Original
2010
Cited alongside, same era.
T. Takayanagi and T. Ugajin, “Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining,” JHEP 1011
Original

Then

M. Z. Hasan and C. L. Kane, ”Colloquium: Topological insulators,” Rev. Mod. Phys. 82
Original
2011
Later among the works it cites.
I. Heemskerk and J. Polchinski, “Holographic and Wilsonian Renormalization Groups,” JHEP 1106
Original
2011
Later among the works it cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
Original
2012
Later among the works it cites.
B. Swingle, “Entanglement Renormalization and Holography,” Phys. Rev. D 86
Original
2012
Later among the works it cites.
M. Nozaki, S. Ryu and T. Takayanagi, “Holographic Geometry of Entanglement Renormalization in Quantum Field Theories,” JHEP 1210
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2010

Cited alongside, same era.

F. Pollmann, E. Berg, A. M. Turner, M. Oshikawa, “Entanglement spectrum of a topological phase in one dimension,” Phys. Rev. B 81

Original

2010

Cited alongside, same era.

A. P. Schnyder, S. Ryu, A. Furusaki, A. W. W. Ludwig, “Classification of topological insulators and superconductors in three spatial dimensions,” Phys. Rev. B 73

Original

2010

Cited alongside, same era.

T. Takayanagi, “Holographic Dual of BCFT,” Phys. Rev. Lett. 107

Original

2011

Cited alongside, same era.

J. Haegeman, T. J. Osborne, H. Verschelde and F. Verstraete, “Entanglement renormalization for quantum fields,” arXiv:1102.5524 [hep-th]

Original

Cited in the paper.

X. -L. Qi, “Exact holographic mapping and emergent space-time geometry,” arXiv:1309.6282 [hep-th]

Original

Cited in the paper.

H. Matsueda, M. Ishihara and Y. Hashizume, “Tensor Network and Black Hole,” arXiv:1208.0206 [hep-th]; H. Matsueda, “Multiscale Entanglement Renormalization Ansatz for Kondo Problem,” arXiv:1208.2872 [cond-mat.stat-mech]

Original

Cited in the paper.

B. Swingle, “Constructing holographic spacetimes using entanglement renormalization,” arXiv:1209.3304 [hep-th]

Original

Cited in the paper.

2012

Later among the works it cites.

X.-L. Qi, H. Katsura, and A. W. W. Ludwig, “General Relationship between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States,” Phys. Rev. Lett. 108

2012

Later among the works it cites.

J. Molina-Vilaplana and P. Sodano, “Holographic View on Quantum Correlations and Mutual Information between Disjoint Blocks of a Quantum Critical System,” JHEP 1110

Original

2013

Later among the works it cites.

A. Mollabashi, M. Nozaki, S. Ryu and T. Takayanagi, “Holographic Geometry of cMERA for Quantum Quenches and Finite Temperature,” JHEP 1403

Original

2014

Closest in time.