Concept record · edition 0.1.0
Area law
A scaling property in which the entanglement entropy of a region grows with the size of its boundary rather than its volume.
Why it matters
It is the structural reason a bounded bond dimension can suffice: it is proven for gapped one-dimensional local Hamiltonians.
What this does not establish
The proven 1D result does not transfer wholesale to higher dimensions or to gapless systems, and volume-law states are outside the regime where a small D helps.
Claims using this concept
- tn-002 · Established resultThe one-dimensional area law proves that ground states of gapped one-dimensional local Hamiltonians have entanglement bounded independently of system size.
- tn-010 · Established resultTensor-network time evolution is limited by entanglement growth, which forces the bond dimension upward as the simulated time increases.
Sources
primary paper · identifier verified
An Area Law for One Dimensional Quantum Systems
M. B. Hastings · 2007
arXiv:0705.2024
Proves the one-dimensional area law that explains why a bounded bond dimension suffices for gapped 1D ground states — and, by implication, when it does not.
Source record →review article · identifier verified
A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
Román Orús · 2013
arXiv:1306.2164
Review covering tensor-network structure, entanglement scaling, and contraction strategy; the general reference for this atlas.
Source record →