On entanglement entropy in arithmetic Chern-Simons theory:
Identification of a contribution to entanglement entropy at absolute zero which is independent of the subsystem‘s size (“topological entanglement entropy”, “long-range entanglement”), reflecting topological order and proportional to the total quantum dimension of anyon excitations:
Alexei Kitaev, John Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96 (2006) 110404 (arXiv:hep-th/0510092)
Michael Levin, Xiao-Gang Wen, Detecting topological order in a ground state wave function, Phys. Rev. Lett., 96, 110405 (2006) arXiv:cond-mat/0510613, doi:10.1103/PhysRevLett.96.110405
(in view of string-net models)
Review:
Shunsuke Furukawa, Entanglement Entropy in Conventional and Topological Orders, talk at Topological Aspects of Solid State Physics 2008 (pdf, pdf)
Tarun Grover, Entanglement entropy and strongly correlated topological matter, Modern Physics Letters A 28 05 (2013) 1330001 doi:10.1142/S0217732313300012
Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen:
Sec. 5 of: Quantum Information Meets Quantum Matter – From Quantum Entanglement to Topological Phases of Many-Body Systems, Quantum Science and Technology (QST), Springer (2019) arXiv:1508.02595, doi:10.1007/978-1-4939-9084-9
In terms of Renyi entropy (it’s independent of the Renyi entropy parameter):
and in the example of Chern-Simons theory:
Discussion in the dimer model:
Discussion via holographic entanglement entropy:
Ari Pakman, Andrei Parnachev, Topological Entanglement Entropy and Holography, JHEP 0807: 097 (2008) (arXiv:0805.1891)
Andrei Parnachev, Napat Poovuttikul, Topological Entanglement Entropy, Ground State Degeneracy and Holography, Journal of High Energy Physics volume 2015, Article number: 92 (2015) (arXiv:1504.08244)
See also:
Relation of long-range entanglement to strong interaction:
Jan Zaanen, Yan Liu, Ya-Wen Sun, Koenraad Schalm, Holographic Duality in Condensed Matter Physics, Cambridge University Press 2015 doi:10.1017/CBO9781139942492
In a way it appears obvious that the strongly interacting bosonic quantum critical state is subject to long-range entanglement. Nonetheless, the status of this claim is conjectural.
It is at present impossible to arrive at more solid conclusions that are based on rigorous mathematical procedures. It does illustrate emphatically the central challenge in the pursuit of field-theoretical quantum information: there are as yet not general measures available to precisely enumerate the meaning of long-range entanglement in such seriously quantum field-theoretical systems. p. 527
Tsung-Cheng Lu, Sagar Vijay, Characterizing Long-Range Entanglement in a Mixed State Through an Emergent Order on the Entangling Surface arXiv:2201.07792
strongly interacting quantum phases of matter at zero temperature can exhibit universal patterns of long-range entanglement
On characterizing anyon braiding / modular transformations on topologically ordered ground states by analysis of (topological) entanglement entropy of subregions:
Yi Zhang, Tarun Grover, Ari M. Turner, Masaki Oshikawa, Ashvin Vishwanath, Quasiparticle statistics and braiding from ground-state entanglement, Phys. Rev. B 85 (2012) 235151 doi:10.1103/PhysRevB.85.235151
Yi Zhang, Tarun Grover, Ashvin Vishwanath, General procedure for determining braiding and statistics of anyons using entanglement interferometry, Phys. Rev. B 91 (2015) 035127 arXiv:1412.0677, doi:10.1103/PhysRevB.91.035127
Zhuan Li, Roger S. K. Mong, Detecting topological order from modular transformations of ground states on the torus, Phys. Rev. B 106 (2022) 235115 [doi:10.1103/PhysRevB.106.235115, arXiv:2203.04329]
Experimental observation:
A. Hamma, W. Zhang, S. Haas, and D. A. Lidar, Entanglement, fidelity, and topological entropy in a quantum phase transition to topological order, Phys. Rev. B 77, 155111 (2008) (doi:10.1103/PhysRevB.77.155111, arXiv:0705.0026)
Hong-Chen Jiang, Zhenghan Wang, Leon Balents, Identifying Topological Order by Entanglement Entropy, Nature Physics 8 902-905 (2012) arXiv:1205.4289
Detection of long-range entanglement entropy in quantum simulations on quantum computers:
Realizing topologically ordered states on a quantum processor, Science 374 6572 (2021) 1237-1241 doi:10.1126/science.abi8378
Probing topological spin liquids on a programmable quantum simulator, Science 374 6572 (2021) 1242-1247 doi:10.1126/science.abi8794
exposition in:
Last revised on February 29, 2024 at 06:01:33. See the history of this page for a list of all contributions to it.