Universal corrections to the entanglement entropy in gapped quantum spin chains: a numerical study

Levi, E., Castro-Alvaredo, O. & Doyon, B. (2013). Universal corrections to the entanglement entropy in gapped quantum spin chains: a numerical study. Physical Review B: Condensed Matter and Materials Physics, 88(9), doi: 10.1103/PhysRevB.88.094439

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We carry out a numerical study of the bipartite entanglement entropy in the gapped regime of two paradigmatic quantum spin chain models: the Ising chain in an external magnetic field and the antiferromagnetic XXZ model. The universal scaling limit of these models is described by the massive Ising field theory and the SU(2)-Thirring (sine-Gordon) model, respectively. We may therefore exploit quantum field theoretical results to predict the behavior of the entropy. We numerically confirm that in the scaling limit, corrections to the saturation of the entropy at large region size are proportional to a modified Bessel function of the first kind, K0(2mr), where m is a mass scale (the inverse correlation length) and r the length of the region under consideration. The proportionality constant is simply related to the number of particle types in the universal spectrum. This was originally predicted by J. L. Cardy, O. A. Castro-Alvaredo, and B. Doyon [ J. Stat. Phys. 130 129 (2008)] and B. Doyon [ Phys. Rev. Lett. 102 031602 (2009)] for two-dimensional quantum field theories. Away from the universal region our numerics suggest an entropic behavior following quite closely the quantum field theory prediction, except for extra dependencies on the correlation length.

Item Type: Article
Subjects: Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/2857

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