Ground state entanglement in quantum spin chains

By José I. Latorre, E. Rico, Guifré Vidal. Quantum information & computation, 2003

460 citations recorded by the source corpus.

A microscopic calculation of ground state entanglement for the XY and Heisenbergmodels shows the emergence of universal scaling behavior at quantum phase transitions,Entanglement is thus controlled by conformal symmetry, Away from the critical point,entanglement gets saturated by a mass scale, Results borrowed from conformal fieldtheory imply irreversibility of entanglement loss along renormalization group trajecto-ries. Entanglement does not saturate in higher dimensions which appears to limit thesuccess of the density matrix renormalization group technique. A possible connection be-tween majorization and renormalization group irreversibility emerges from our numericalanalysis.

View Paper: https://www.semanticscholar.org/paper/78fcbb40efa346ef94160d1bd00961de55112b1b

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Citations in the corpus

• Holographic entanglement entropy: an overview (2009, background): “Indeed, in two-dimensional conformal field theory, the universal piece of entanglement entropy is proportional to the central charge in two-dimensional conformal field theories (2D CFTs) as shown in [21, 22], where a general prescription of computing the entropy in 2D CFTs is given.”
• Aspects of Holographic Entanglement Entropy (2006, methodology): “It was argued that the positivity of C(x) is connected to a majorization relation for local density matrices [3, 4, 44, 45, 46] In our example of the d+ 1 dimensional free field, we can reduce it to infinitely many massive fields in two dimensions.”
• The quantum Ising chain for beginners (2020, background): “The question we address here is how to calculate the entanglement entropy for the quantum Ising chain [20].”
• The density-matrix renormalization group (2004, background): “In fact, Eq. s65d can be linked sGaite, 2003; Latorre et al., 2004d to the geometric entropy sCallan and Wilczek, 1994d of such field theories, Rev. Mod.”