Comb entanglement in quantum spin chains

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.

6 pages, 4 figures

References in corpus (4)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Constructing N-qubit entanglement monotones from anti-linear operators
• Entanglement and Quantum Phase Transition Revisited
• A new correlator in quantum spin chains

Cited by in corpus (3)

• Exact relationship between the entanglement entropies of XY and quantum Ising chains
• Entanglement of two blocks of spins in the critical Ising model
• A new correlator in quantum spin chains