Claim record · edition 0.1.0
tn-002Established result
The one-dimensional area law proves that ground states of gapped one-dimensional local Hamiltonians have entanglement bounded independently of system size.
This is the structural result explaining why DMRG succeeds in one dimension: the entanglement a correct answer must carry does not grow with the chain, so a fixed bond dimension can suffice.
Limits of this claim
The proof covers gapped 1D local Hamiltonians. It does not transfer wholesale to higher dimensions or to gapless systems, and it says nothing about states reached by long-time evolution.
Supporting 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.
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