Ground states of unfrustrated spin Hamiltonians satisfy an area law
- 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.
| Author details: | Niel de Beaudrap, Tobias J. Osborne, Jens Eisert |
|---|---|
| URL: | http://iopscience.iop.org/1367-2630 |
| DOI: | https://doi.org/10.1088/1367-2630/12/9/095007 |
| ISSN: | 1367-2630 |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2010 |
| Publication year: | 2010 |
| Release date: | 2017/03/25 |
| Source: | New journal of physics. - ISSN 1367-2630. - 12 (2010), 9, Art. 095007 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| Peer review: | Referiert |
| Publishing method: | Open Access |
