TY  - JOUR
A1  - de Beaudrap, Niel
A1  - Osborne, Tobias J.
A1  - Eisert, Jens
T1  - Ground states of unfrustrated spin Hamiltonians satisfy an area law
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.
Y1  - 2010
UR  - http://iopscience.iop.org/1367-2630
U6  - https://doi.org/10.1088/1367-2630/12/9/095007
SN  - 1367-2630
ER  - 
TY  - JOUR
A1  - de Beaudrap, Niel
A1  - Ohliger, Matthias
A1  - Osborne, Tobias J.
A1  - Eisert, Jens
T1  - Solving frustration-free spin systems
N2  - We identify a large class of quantum many-body systems that can be solved exactly: natural frustration-free spin-1/2 nearest-neighbor Hamiltonians on arbitrary lattices. We show that the entire ground-state manifold of such models can be found exactly by a tensor network of isometries acting on a space locally isomorphic to the symmetric subspace. Thus, for this wide class of models, real-space renormalization can be made exact. Our findings also imply that every such frustration-free spin model satisfies an area law for the entanglement entropy of the ground state, establishing a novel large class of models for which an area law is known. Finally, we show that our approach gives rise to an ansatz class useful for the simulation of almost frustration-free models in a simple fashion, outperforming mean- field theory.
Y1  - 2010
UR  - http://prl.aps.org/
U6  - https://doi.org/10.1103/Physrevlett.105.060504
SN  - 0031-9007
ER  -