Comb entanglement in quantum spin chains

J. P. Keating, F. Mezzadri, and M. Novaes
Phys. Rev. A 74, 012311 – Published 18 July 2006

Abstract

Bipartite entanglement in the ground state of a chain of N quantum spins can be quantified either by computing pairwise concurrence or by dividing the chain into two complementary subsystems. In the latter case the smaller subsystem is usually a single spin or a block of adjacent spins and the entanglement differentiates between critical and noncritical regimes. Here we extend this approach by considering a more general setting: our smaller subsystem SA consists of a comb of L spins, spaced p sites apart. Our results are thus not restricted to a simple area law, but contain nonlocal information, parametrized by the spacing p. For the XX model we calculate the von Neumann entropy analytically when N and investigate its dependence on L and p. We find that an external magnetic field induces an unexpected length scale for entanglement in this case.

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  • Received 5 April 2006

DOI:https://doi.org/10.1103/PhysRevA.74.012311

©2006 American Physical Society

Authors & Affiliations

J. P. Keating*, F. Mezzadri, and M. Novaes

  • School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom

  • *Electronic address: j.p.keating@bristol.ac.uk
  • Electronic address: f.mezzadri@bristol.ac.uk
  • Electronic address: marcel.novaes@bristol.ac.uk

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Issue

Vol. 74, Iss. 1 — July 2006

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