Topological entanglement entropy.
By Alexei Y. Kitaev, John Preskill. Physical Review Letters, 2005
1,993 citations recorded by the source corpus.
We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity. We show that - gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/40127d4057c355ecdba28278c7e854f3c202f29a
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Citations in the corpus
- Comments on quantum gravity and entanglement (2009, background): “Indeed, in certain cases (specifically in 2+1 dimensional field theories, for sufficiently large regions A,B,C) I(A,B,C) is exactly the quantity that defines topological entanglement entropy [33], a useful order parameter for some quantum phase transitions.”
- Gravitation from entanglement in holographic CFTs (2013, background): “This was motivated in part by the importance of quantum entanglement for understanding quantum phases of matter in condensed matter systems [12–15].”
- Black holes and the butterfly effect (2013, methodology): “= tr[ρAB(U) (2)]− 2 |A|2 tr[ρAB] + 1 |A|4 tr[1] (A.”
- Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids (2008, methodology): “We thank Paul Fendley, Eun-Ah Kim, Alexei Kitaev, Michael Levin, Joel Moore, Chetan Nayak, Stefanos Papanikolaou, John Preskill, and Kirill Shtengel for many discussions.”
- Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory (2023, methodology): “We adopt the Kitaev-Preskill prescription to extract γN [45].”
- Entanglement entropy in quantum impurity systems and systems with boundaries (2009, background): “Note that the extra term (1/3) ln r does not occur in the formulation of [18, 19]”
- Aspects of holography for theories with hyperscaling violation (2012, background): “More generally, sub-leading but cutoff independent terms in the entanglement entropy have proved to be of significant interest – for instance, they can distinguish between states with different topological orders [31, 32].”
- Shape dependence of entanglement entropy in conformal field theories (2015, methodology): “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.”
- The holographic entropy cone (2015, background): “, difference of the left- and right-hand side of the monogamy inequality) specializes to the topological entanglement entropy [50].”
- Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence. (2006, background): “For example, in a modern trend of condensed matter physics it has been becoming clear that quantum phases of matter need to be characterized by their pattern of entanglement encoded in many-body wave functions of ground states, rather than conventional order parameters [7, 8, 9].”