Stability of global entanglement in thermal states of spin chains

• Published in: Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2004-11, Vol.70 (5), Article 052303
• Main Authors: Brennen, Gavin, Bullock, Stephen
• Format: Article
• Language: English
• Subjects: ATOMIC AND MOLECULAR PHYSICS; CORRELATIONS; DISTURBANCES; GROUND STATES; HAMILTONIANS; J-J COUPLING; LATTICE FIELD THEORY; MAGNETIC FIELDS; MATERIALS SCIENCE; MIXED STATE; ONE-DIMENSIONAL CALCULATIONS; QUANTUM MECHANICS; SPIN; STABILITY
• ISSN: 1050-2947; 1094-1622
• DOI: 10.1103/PhysRevA.70.052303

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.