Fetching the paper…

Reading the bibliography…

2015

On the definition of entanglement entropy in lattice gauge theories

Aoki, Sinya, Iritani, Takumi, Nozaki, Masahiro et al.

Original
PDF
Post on X

Understand

We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well.

Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories.
We then derive the associated replica formula.
We also discuss the issue of gauge invariance of the entanglement entropy.

On the definition of entanglement entropy in lattice gauge theories · Around

Built on

M. Creutz, “Gauge fixing, the transfer matrix and confinement on a lattice”, Phys. Rev. D15, 1128 (1977)
1977
Earlier work this paper cites.
M. Lüsher, “Construction of a selfadjoint, strictly positive transfer matrix for Euclidean lattice gauge theories,” Comm. Math. Phys. 54, 283(1977)
1977
Earlier work this paper cites.
L. Susskind and J. Uglum, “Black hole entropy in canonical quantum gravity and superstring theory,” Phys. Rev. D 50
1994
Earlier work this paper cites.
D. N. Kabat and M. J. Strassler, “A Comment on entropy and area,” Phys. Lett. B 329
1994
Earlier work this paper cites.
D. N. Kabat, “Black hole entropy and entropy of entanglement,” Nucl. Phys. B 453
1995
Earlier work this paper cites.
R. W. Carter, I. G. MacDonald and G. B. Segal, in “Lectures on Lie groups and Lie algebras,” Cambridge University Press, 1995
1995
Earlier work this paper cites.
See, for example: M. A. Nielsen and I. L. Chuang, “Quantum computation and quantum information,” Cambridge University Press, Cambridge, 2000
2000
Earlier work this paper cites.
A. Hamma, R. Ionicioiu, P. Zanardi, “Ground state entanglement and geometric entropy in the Kitaev’s model,” Phys. Lett. A 337
2005
Earlier work this paper cites.
A. Hamma, R. Ionicioiu, P. Zanardi, “Biparticle entanglement and entropic boundary law in lattice spin systems,” Phys. Rev. A 71
2005
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP 0608
2006
Earlier work this paper cites.
M. Levin and X. G. Wen, “Detecting Topological Order in a Ground State Wave Function,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
A. Kitaev and J. Preskill, “Topological entanglement entropy,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.

Similar

T. Nishioka and T. Takayanagi, “AdS Bubbles, Entropy and Closed String Tachyons,” JHEP 0701
2007
Cited alongside, same era.
H. Li and F. D. M. Haldane, “Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States,” Phys. Rev. Lett. 101
Original
2008
Cited alongside, same era.
I. R. Klebanov, D. Kutasov and A. Murugan, “Entanglement as a probe of confinement,” Nucl. Phys. B 796
Original
2008
Cited alongside, same era.
P. V. Buividovich and M. I. Polikarpov, “Entanglement entropy in gauge theories and holographic principle for electric strings,” Phys, Lett. B 670
2008
Cited alongside, same era.
P. V. Buividovich and M. I. Polikarpov, “Numerical study of entanglement entropy in SU(2) lattice gauge theory,” Nucl. Phys. B 802
Original

Then

N. Shiba, “Entanglement Entropy of Two Black Holes and Entanglement Entropic Force,” Phys. Rev. D 83
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.
N. Shiba, “Entanglement Entropy of Two Spheres,” JHEP 1207
Original
2012
Later among the works it cites.
A. Lewkowycz, “Holographic Entanglement Entropy and Confinement,” JHEP 1205
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…

2008

Cited alongside, same era.

B. Hsu, M. Mulligan, E. Fradkin and E.A. Kim, “Universal entanglement entropy in 2D conformal quantum critical points,” Phys. Rev. B 79

2009

Cited alongside, same era.

S. T. Flammia, A. Hamma, T. L. Hughes, and X.-G. Wen, “Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure,” Phys. Rev. Lett. 103

2009

Cited alongside, same era.

Y. Nakagawa, A. Nakamura, S. Motoki and V. I. Zakharov, “Entanglement entropy of SU(3) Yang-Mills theory”, PoS LAT 2009

2009

Cited alongside, same era.

M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42

2010

Cited alongside, same era.

M. B. Hastings, I. Gonzalez, A. B. Kallin, and R. G. Melko, “Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations,” Phys. Rev. Lett. 104

2010

Cited alongside, same era.

Y. Nakagawa, A. Nakamura, S. Motoki, V.I. Zakharov, “Quantum entanglement in SU(3) lattice Yang-Mills theory at zero and finite temperatures,” PoS Lattice2010, 281 (2010)

2010

Cited alongside, same era.

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

Cited in the paper.

2012

Later among the works it cites.

W. Donnelly, “Decomposition of entanglement entropy in lattice gauge theories”, Phys. Rev. D 85

2012

Later among the works it cites.

M. Nozaki, T. Numasawa, A. Prudenziati and T. Takayanagi, “Dynamics of Entanglement Entropy from Einstein Equation,” Phys. Rev. D 88

2013

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

2014

Later among the works it cites.

T. Faulkner, M. Guica, T. Hartman, R. C. Myers and M. Van Raamsdonk, “Gravitation from Entanglement in Holographic CFTs,” JHEP 1403

2014

Later among the works it cites.

T. Nishioka, “Relevant Perturbation of Entanglement Entropy and Stationarity,” Phys. Rev. D 90

Original

2014

Later among the works it cites.

V. Rosenhaus and M. Smolkin, “Entanglement Entropy: A Perturbative Calculation,” JHEP 1412

2014

Later among the works it cites.