Energy as an Entanglement Witnesses for One Dimensional XYZ Heisenberg Lattice: Optimization Approach

Abstract

If energy ensemble average is less than the minimum energy of separable states, the system is entangled. In this study, we consider energy as an entanglement witness for one dimensional XYZ Heisenberg lattice up to ten qubits analytically. We find minimum of energy using Lagrange undetermined multipliers to construct the entanglement witness. We also find threshold temperature and magnetic field, for which below them the system is entangled. The results are in good agreement with the literature. For systems with more than six qubits, the results show temperature gets a stable value for a zero magnetic field.

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Correspondence to K. Aghayar.

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Homayoun, T., Aghayar, K. Energy as an Entanglement Witnesses for One Dimensional XYZ Heisenberg Lattice: Optimization Approach. J Stat Phys 176, 85–93 (2019). https://doi.org/10.1007/s10955-019-02289-1

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Keywords

  • Entanglement witness
  • Heisenberg lattice
  • Lagrange undetermined multipliers