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Comb entanglement in quantum spin chains

J. P. Keating·F. Mezzadri·M. Novaes
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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 non-critical regimes. Here we extend this approach by considering a more general setting: our smaller subsystem $S_A$ consists of a {\it comb} of $L$ spins, spaced $p$ sites apart. Our results are thus not restricted to a simple `area law', but contain non-local information, parameterized by the spacing $p$. For the XX model we calculate the von-Neumann entropy analytically when $N\to \infty$ 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.

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J. P. Keating, F. Mezzadri, M. Novaes. 2006-04-04. Comb entanglement in quantum spin chains. https://doi.org/10.1103/physreva.74.012311

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