Entanglement and alpha entropies for a massive Dirac field in two dimensions
By H. Casini, C. Fosco, M. Huerta. 2005
287 citations recorded by the source corpus.
We present some exact results on universal quantities derived from the local density matrix ρ, for a free massive Dirac field in two dimensions. We first find trρn in a novel fashion, which involves the correlators of suitable operators in the sine–Gordon model. These, in turn, can be written exactly in terms of the solutions of non-linear differential equations of the Painlevé V type. Equipped with the previous results, we find the leading terms for the entanglement entropy, both for short and long distances, and showing that in the intermediate regime it can be expanded in a series of multiple integrals. The previous results have been checked by direct numerical calculations on the lattice, finding perfect agreement. Finally, we comment on a possible generalization of the entanglement entropy c-theorem to the alpha-entropies.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/7476507ff0ca0b55236d9e8075241e0cb19e3c11
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In Atomic and Molecular Physics, and Optics
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Citations in the corpus
- Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases (2016, background): “However, in the case of the massless free fermion fieldtheory, this two-point function in the half plane simplifies considerably and our desired object boils down to [30,58] (up to unimportant multiplicative constants) 〈Tn(z1)T̃n(z2)〉= e−σ(z1) d g(z1) dz1 e−σ(z2) d g(z2) dz2 |g(z1)− g(z2)|(2) Im(g(z”
- Form Factors of Branch-Point Twist Fields in Quantum Integrable Models and Entanglement Entropy (2007, methodology): “Note that for the free case our result is in agreement with the n→ 1 limit evaluated in [21].”
- Symmetry resolved entanglement in free fermionic systems (2019, background): “The relation between twisted boundary conditions and flux insertion was actually previously explored, for example, in the context of free field theories [18–20].”
- Remarks on the entanglement entropy for disconnected regions (2008, background): “Remarkably, this specific form of the entropy gives an extensive mutual information [2], I(A,B ∪ C) = I(A,B) + I(A,C) .”
- Aspects of Holographic Entanglement Entropy (2006, methodology): “For massive free fermions and scalar fields, the function C is characterized as a solution to a differential equation of Painleve V type and its numerical form can be found in [37, 39].”
- Notes on islands in asymptotically flat 2d dilaton black holes (2020, methodology): “The explicit formula for free Dirac fermion is given by [28]”
- Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions (2021, background): “(G9) for Hermitian systems has been derived in several previous works [77, 82, 94].”
- Islands in Schwarzschild black holes (2020, background): “(ii) When the distance L between the parallelly placed boundary (hyper)surfaces of A and B is sufficiently small, the mutual information I(A;B) is given by [39, 40]”
- Entanglement entropy of two disjoint blocks in XY chains (2010, background): “fermion theories [7]–[9], and only the calculations within more complex theories allowed us to detect this error [10]–[13].”
- Holographic mutual information is monogamous (2011, methodology): “For a free massless fermion in two dimensions, the entanglement entropy of an arbitrary collection of intervals was computed in [14, 15], and the result implies I3(A : B : C) = 0 for any A,B,C.”