Built on

R. Savit, “Duality in Field Theory and Statistical Systems,” Rev. Mod. Phys. 52
1980
Earlier work this paper cites.
M. Ohya and D. Petz, “Quantum Entropy and its Use,” Springer, 2004
2004
Earlier work this paper cites.
A. Hamma, R. Ionicioiu and P. Zanardi, “Bipartite entanglement and entropic boundary law in lattice spin systems,” Phys. Rev. A 71
2005
Earlier work this paper cites.
A. Kitaev and J. Preskill, “Topological entanglement entropy,” Phys. Rev. Lett. 96
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
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A. Hamilton, D. N. Kabat, G. Lifschytz and D. A. Lowe, “Holographic representation of local bulk operators,” Phys. Rev. D 74
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P. V. Buividovich and M. I. Polikarpov, “Entanglement entropy in lattice gauge theories,” PoS Confinment 8
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Earlier work this paper cites.
D. Kabat, G. Lifschytz and D. A. Lowe, “Constructing local bulk observables in interacting AdS/CFT,” Phys. Rev. D 83
Original
2011
Earlier work this paper cites.

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2016

Entanglement Entropy and Duality

Radicevic, Djordje

Understand

Using the algebraic approach to entanglement entropy, we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality.

Our main result is that a maximal algebra of observables in a region typically dualizes to a non-maximal algebra in a dual region.
In particular, we show how the usual notion of tracing out external degrees of freedom dualizes to a tracing out coupled to an additional summation over superselection sectors.
We briefly comment on possible extensions of our results to more intricate dualities, including holographic ones.

Built on

R. Savit, “Duality in Field Theory and Statistical Systems,” Rev. Mod. Phys. 52
1980
Earlier work this paper cites.
M. Ohya and D. Petz, “Quantum Entropy and its Use,” Springer, 2004
2004
Earlier work this paper cites.
A. Hamma, R. Ionicioiu and P. Zanardi, “Bipartite entanglement and entropic boundary law in lattice spin systems,” Phys. Rev. A 71
2005
Earlier work this paper cites.
A. Kitaev and J. Preskill, “Topological entanglement entropy,” Phys. Rev. Lett. 96
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. Hamilton, D. N. Kabat, G. Lifschytz and D. A. Lowe, “Holographic representation of local bulk operators,” Phys. Rev. D 74
2006
Earlier work this paper cites.
P. V. Buividovich and M. I. Polikarpov, “Entanglement entropy in gauge theories and the holographic principle for electric strings,” Phys. Lett. B 670
Original
2008
Earlier work this paper cites.
P. V. Buividovich and M. I. Polikarpov, “Entanglement entropy in lattice gauge theories,” PoS Confinment 8
Original
2009
Earlier work this paper cites.
D. Kabat, G. Lifschytz and D. A. Lowe, “Constructing local bulk observables in interacting AdS/CFT,” Phys. Rev. D 83
Original
2011
Earlier work this paper cites.