Ground states of unfrustrated spin Hamiltonians satisfy an area law

New Journal of Physics (Impact Factor: 3.56). 09/2010; 12(9). DOI: 10.1088/1367-2630/12/9/095007
Source: arXiv


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.

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