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| Three dimensional Heisenberg model in the form of a
tetrahedron lattice is investigated. The concurrence and
multipartite entanglement are calculated through 2-concurrence $C$
and 4-concurrence $C_4$. The concurrence $C$ and multipartite
entanglement $C_4$ depend on different coupling strengths $J_i$
and are decreased when the temperature $T$ is increased. For a
symmetric tetrahedron lattice, the concurrence $C$ is symmetric
about $J_1$ when $J_2$ is negative while the multipartite
entanglement $C_4$ is symmetric about $J_1$ when $J_2<2$. For a
regular tetrahedron lattice, the concurrence $C$ of ground state
is $\frac{1}{3}$ for ferromagnetic case while $C=0$ for
antiferromagnetic case. However, there is no multipartite
entanglement since $C_4 =0$ in a regular tetrahedron lattice. The
external magnetic field $B$ can increase the maximum value of the
concurrence $C_B$ and induce two or three peaks in $C_B$. There is
a peak in the multipartite entanglement $C_{4B}$ when $C_{4B}$ is
varied as a function of the temperature $T$. This peak is mainly
induced by the magnetic field $B$ |
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| Keywords: multipartite entanglement, concurrence, three dimensions, tetrahedron lattice |
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