Article

Ground states of unfrustrated spin Hamiltonians satisfy an area law

New Journal of Physics (Impact Factor: 4.06). 09/2010; DOI: 10.1088/1367-2630/12/9/095007
Source: arXiv

ABSTRACT We show that ground states of unfrustrated quantum spin-1/2 systems on general lattices satisfy an entanglement area law, provided that the Hamiltonian can be decomposed into nearest-neighbor interaction terms which have entangled excited states. The ground state manifold can be efficiently described as the image of a low-dimensional subspace of low Schmidt measure, under an efficiently contractible tree-tensor network. This structure gives rise to the possibility of efficiently simulating the complete ground space (which is in general degenerate). We briefly discuss "non-generic" cases, including highly degenerate interactions with product eigenbases, using a relationship to percolation theory. We finally assess the possibility of using such tree tensor networks to simulate almost frustration-free spin models. Comment: 14 pages, 4 figures

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