Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids

By Shiying Dong, E. Fradkin, R. Leigh, S. Nowling. 2008

173 citations recorded by the source corpus.

We compute directly the entanglement entropy of spatial regions in Chern-Simons gauge theories in 2+1 dimensions using surgery. We use these results to determine the universal topological piece of the entanglement entropy for Abelian and non-Abelian quantum Hall fluids.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/f44991ca0b0bb7cb06bcaae5fec16eb2af3f6835

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In Atomic and Molecular Physics, and Optics

1. T. Nishioka
2. T. Takayanagi
3. J. Alicea
4. William Donnelly
5. S. Ryu
6. N. Lindner
7. A. Stern
8. C. Nayak

Citations in the corpus

• Quantum Hall physics : Hierarchies and conformal field theory techniques (2016, background): “22 For a mathematical perspective on topological entanglement entropy in Chern-Simons theories and quantum Hall states, see (Dong et al., 2008) and (Hikami, 2008).”
• Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy (2009, background): “The topological entanglement entropy is a quantity that can be computed from a given ground state of the FQHE or the Chern-Simons effective field theory [25, 26, 27], and encodes information on the type of quasi-particles (topological excitations) that can be build on the ground state.”
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure (2013, background): “This invariant can be further decomposed as γ = log( D /d Ψ ) , where d Ψ is the quantum dimension of the quasiparticle corresponding to the state | Ψ , and D is the ‘total quantum di-mension’ of the phase [138–140].”
• Shape dependence of entanglement entropy in conformal field theories (2015, unknown): “We show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, and proportional to the coefficient CT appearing in the two-point function of stress tensors in that CFT.”
• Holographic entanglement entropy: an overview (2009, methodology): “The calculations based on the surgery method in Chern-Simons gauge theory [130] have been performed in [131].”
• Entanglement entropy and nonabelian gauge symmetry (2014, methodology): “This is essential in order to give agreement with Chern-Simons theories [37] and the holographic entanglement entropy [5], whose derivations are based on the replica trick.”