Stability of Global Entanglement in Thermal States of Spin Chains
G K. Brennen, Stephen Bullock
We investigate the entanglement properties of a one dimensional chain of spin qubits coupled via nearest neighbor 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 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 non zero entanglement.
Physical Review A (Atomic, Molecular and Optical Physics)