dorsal/arxiv
View SchemaBipartite entanglement and entropic boundary law in lattice spin systems
| Authors | Alioscia Hamma, Radu Ionicioiu, Paolo Zanardi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409073 |
| URL | https://arxiv.org/abs/quant-ph/0409073 |
| DOI | 10.1103/PhysRevA.71.022315 |
| Journal | Phys. Rev. A 71, 022315 (2005) |
Abstract
We investigate bipartite entanglement in spin-1/2 systems on a generic lattice. For states that are an equal superposition of elements of a group $G$ of spin flips acting on the fully polarized state $\ket{0}^{\otimes n}$, we find that the von Neumann entropy depends only on the boundary between the two subsystems $A$ and $B$. These states are stabilized by the group $G$. A physical realization of such states is given by the ground state manifold of the Kitaev's model on a Riemann surface of genus $\mathfrak{g}$. For a square lattice, we find that the entropy of entanglement is bounded from above and below by functions linear in the perimeter of the subsystem $A$ and is equal to the perimeter (up to an additive constant) when $A$ is convex. The entropy of entanglement is shown to be related to the topological order of this model. Finally, we find that some of the ground states are absolutely entangled, i.e., no partition has zero entanglement. We also provide several examples for the square lattice.
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"abstract": "We investigate bipartite entanglement in spin-1/2 systems on a generic\nlattice. For states that are an equal superposition of elements of a group $G$\nof spin flips acting on the fully polarized state $\\ket{0}^{\\otimes n}$, we\nfind that the von Neumann entropy depends only on the boundary between the two\nsubsystems $A$ and $B$. These states are stabilized by the group $G$. A\nphysical realization of such states is given by the ground state manifold of\nthe Kitaev\u0027s model on a Riemann surface of genus $\\mathfrak{g}$. For a square\nlattice, we find that the entropy of entanglement is bounded from above and\nbelow by functions linear in the perimeter of the subsystem $A$ and is equal to\nthe perimeter (up to an additive constant) when $A$ is convex. The entropy of\nentanglement is shown to be related to the topological order of this model.\nFinally, we find that some of the ground states are absolutely entangled, i.e.,\nno partition has zero entanglement. We also provide several examples for the\nsquare lattice.",
"arxiv_id": "quant-ph/0409073",
"authors": [
"Alioscia Hamma",
"Radu Ionicioiu",
"Paolo Zanardi"
],
"categories": [
"quant-ph",
"cond-mat.str-el"
],
"doi": "10.1103/PhysRevA.71.022315",
"journal_ref": "Phys. Rev. A 71, 022315 (2005)",
"title": "Bipartite entanglement and entropic boundary law in lattice spin systems",
"url": "https://arxiv.org/abs/quant-ph/0409073"
},
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