Stability of global entanglement in thermal states of spin chains

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 'g...

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Bibliographic Details
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
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Summary: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.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.70.052303