Stability of global entanglement in thermal states of spin chains

Gavin K. Brennen and Stephen S. Bullock
Phys. Rev. A 70, 052303 – Published 4 November 2004

Abstract

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 -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 -concurrence of ground states when the interaction is subject to a time-reversal antisymmetric magnetic field perturbation. The -concurrence in the ground state of the isotropic 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 -concurrence for thermal mixed states is derived and a threshold temperature is computed below which the system has nonzero entanglement.

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  • Received 22 June 2004

DOI:https://doi.org/10.1103/PhysRevA.70.052303

Authors & Affiliations

Gavin K. Brennen1,* and Stephen S. Bullock2,†

  • 1National Institute of Standards and Technology, Atomic Physics Division, Gaithersburg, Maryland 20899-8420, USA
  • 2National Institute of Standards and Technology, Mathematical and Computational Sciences Division, Gaithersburg, Maryland 20899-8910, USA

  • *Electronic address: gavin.brennen@nist.gov
  • Electronic address: stephen.bullock@nist.gov

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Issue

Vol. 70, Iss. 5 — November 2004

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