Entanglement spectrum in one-dimensional systems
By Pasquale Calabrese, A. Lefevre. 2008
293 citations recorded by the source corpus.
We derive the distribution of eigenvalues of the reduced density matrix of a block of length $\ensuremath{\ell}$ in a one-dimensional system in the scaling regime. The resulting ``entanglement spectrum'' is described by a universal scaling function depending only on the central charge of the underlying conformal field theory. This prediction is checked against exact results for the $XX$ chain. We also show how the entanglement gap closes when $\ensuremath{\ell}$ is large.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/a11efc9e719cbffb0363cfbe2003f57f60c449be
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Many-body localization: An introduction and selected topics (2017, unknown): “Note that, whereas the conclusions of this bubble argument seem to be corroborated by the numerics mentioned above, it is not the case for other situations with bubble arguments, most notably the prediction of absence of mobility edge [50] (see Section 1.3).”
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- Entanglement entropy of excited states (2009, background): “However, because of the relative small values of ` we can access, this is not enough to check recent conformal predictions for the spectrum [56].”
- Finite temperature entanglement negativity in conformal field theory (2014, background): “Furthermore, the knowledge of the Rényi entropies for arbitrary n provides also the full spectrum of the reduced density matrix [40].”
- Entanglement entropy of two disjoint intervals in conformal field theory (2009, methodology): “[33] it has been shown that this can be calculated by knowing TrρA for integer n only.”
- Entanglement entropy of two disjoint intervals in conformal field theory: II (2010, background): “the response of the partition function to a scale transformation) under this uniformizing map, one obtains [2, 3] TrρA = cn` − c 6 (n−1/n) , (2) from which the replica trick (1) leads to the famous result (c/3) log ` [5, 6] and to the the full spectrum of ρA [7].”
- Entanglement entropy and conformal field theory (2009, methodology): “• The ratio of the first two eigenvalues (see [102] for details) is λ2 λmax = e = e 6k c ln(l/a) , (71)”
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- Unusual corrections to scaling in entanglement entropy (2010, background): “[2]), and gives more information about the entanglement than the widely studied von Neumann entropy S (1) A .”
- Symmetry resolved entanglement in free fermionic systems (2019, methodology): “[13] exploiting the method of Stieltjes transform [44] which implicitly assumes this approximation.”