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We investigate the entanglement properties of thermal states of the harmonic lattice in one, two and three dimensions.
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The two-point correlation function G ( R → ) G(\vec{R}) measures the correlation between the order-parameter at two positions separated by R → \vec{R} . A solid is characterised by long-range order of the mass density ρ ( x ) \rho(x) . For the harmonic lattice the two-point correlation function can be expressed as G ( R → ) = ∑ k → e i k → ⋅ R → ∑ P → e i k → ⋅ P → ⟨ e i k → ⋅ ( u ^ P → − u ^ 0 → ) ⟩ G(\vec{R})=\sum_{\vec{k}}e^{i\vec{k}\cdot\vec{R}}\sum_{\vec{P}}e^{i\vec{k}\cdot\vec{P}}\langle e^{i\vec{k}\cdot(\hat{u}_{\vec{P}}-\hat{u}_{\vec{0}})}\rangle , which can be calculated explicitly, see for example [ 4 , 22 ]
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D. Cavalcanti, A. Ferraro, A. Garcia-Saez, and A. Acin, Phys. Rev. Lett. 100
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