Comb entanglement in quantum spin chains

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 ->infinity 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.