Entanglement spectrum as a generalization of entanglement entropy: identification of topological order in non-Abelian fractional quantum Hall effect states.

By Hui Li, F. Haldane. Physical Review Letters, 2008

1,202 citations recorded by the source corpus.

We study the "entanglement spectrum" (a presentation of the Schmidt decomposition analogous to a set of "energy levels") of a many-body state, and compare the Moore-Read model wave function for the nu=5/2 fractional quantum Hall state with a generic 5/2 state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions. Their spectra share a common "gapless" structure, related to conformal field theory. In the model state, these are the only levels, while in the "generic" case, they are separated from the rest of the spectrum by a clear "entanglement gap", which appears to remain finite in the thermodynamic limit. We propose that the low-lying entanglement spectrum can be used as a "fingerprint" to identify topological order.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/702dd1a9abcdecf7690d3439147e29eda59c9a68

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Anyons and matrix product operator algebras (2015, background): “information about the topological excitations [14] and that for chiral phases the socalled entanglement spectrum reveals the nature of the edge physics [15].”
Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy) (2018, neutral): “The entanglement spectrum { α} [49] is defined in terms of the spectrum {Λ(2)α} of the reduced density matrix by Λ(2)α = exp(− α) for each α.”
Entanglement temperature and entanglement entropy of excited states (2013, background): “[3] H.”
Eternal traversable wormhole (2018, background): “This is analogous to the usual map between the sphere and the Euclidean cylinder for higher dimensional CFTs.”
Fractional Chern Insulator (2011, methodology): “Away from the model states, like the Coulomb ground state, the ES may exhibits an entanglement gap [21, 24].”
Gapless Symmetry-Protected Topological Order (2017, background): “Then the gTrivial Hamiltonian is (still with Gσ ×Gτ symmetry) HgTrivial = ∑ a∈A Λ(1−Pa)+ ∑ a∈A P ′a (1− σxa)P ′a− ∑ a?”
Measuring entanglement entropy in a quantum many-body system (2015, background): “The Rényi entropies are rapidly gaining importance in theoretical condensed matter physics, as they can be used to extract information about the “entanglement spectrum” [41] providing more complete information about the quantum state than just the von Neuman entropy.”
Locality of temperature (2013, background): “(2), which depends on a parameter τ ∈ [0, 1], provides more information about the correlations between two observables than the standard covariance in a similar way as the class of Rényi entropies characterizes more completely the entanglement properties of a state than simply the von Neumann entrop”
Many-body localization and delocalization in large quantum chains (2018, background): “Here the entanglement eigenvalues λi ≥ 0 [53] are the eigenvalues of the effective entanglement Hamiltonian He defined through the reduced density matrix of the system after tracing out the degrees of freedom of the subsystem B: He = − ln TrBρ [54].”