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arXiv:quant-ph/0604016 · Physical Review A

Comb entanglement in quantum spin chains

Jonathan P. Keating, Francesco Mezzadri, Marcel Novaes

Published Jul 18, 2006• 24 citations
arXivHTMLPDF

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 ${S}_{A}$ 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 $N\ensuremath{\rightarrow}\ensuremath{\infty}$ 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.

DOI
10.1103/physreva.74.012311

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