Details
| Original language | English |
|---|---|
| Article number | 095007 |
| Journal | New Journal of Physics |
| Volume | 12 |
| Publication status | Published - 16 Sept 2010 |
| Externally published | Yes |
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 that 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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: New Journal of Physics, Vol. 12, 095007, 16.09.2010.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Ground states of unfrustrated spin Hamiltonians satisfy an area law
AU - De Beaudrap, Niel
AU - Osborne, Tobias J.
AU - Eisert, Jens
PY - 2010/9/16
Y1 - 2010/9/16
N2 - 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 that 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.
AB - 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 that 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.
UR - http://www.scopus.com/inward/record.url?scp=77958546414&partnerID=8YFLogxK
U2 - 10.1088/1367-2630/12/9/095007
DO - 10.1088/1367-2630/12/9/095007
M3 - Article
AN - SCOPUS:77958546414
VL - 12
JO - New Journal of Physics
JF - New Journal of Physics
SN - 1367-2630
M1 - 095007
ER -