Stability of global entanglement in thermal states of spin chains (12 pages)

We investigate the entanglement properties of a one-dimensional chain of qubits coupled via nearest-neighbor spin-spin interactions. The entanglement measure used is the $n$-concurrence, which is distinct from other measures on spin chains such as bipartite entanglement in that it can quantify ``global'' entanglement across the spin chain. Specifically, it computes the overlap of a quantum state with its time-reversed state. As such, this measure is well suited to study ground states of spin-chain Hamiltonians that are intrinsically time-reversal-symmetric. We study the robustness of $n$-concurrence of ground states when the interaction is subject to a time-reversal antisymmetric magnetic field perturbation. The $n$-concurrence in the ground state of the isotropic $XX$ model is computed and it is shown that there is a critical magnetic field strength at which the entanglement experiences a jump discontinuity from the maximum value to zero. The $n$-concurrence for thermal mixed states is derived and a threshold temperature is computed below which the system has nonzero entanglement.