Abstract
We present a new proof for the 1D area law for frustration-free systems with a constant gap, which exponentially improves the entropy bound in Hastingsâ 1D area law and which is tight to within a polynomial factor. For particles of dimension , spectral gap , and interaction strength at most , our entropy bound is , where . Our proof is completely combinatorial, combining the detectability lemma with basic tools from approximation theory. In higher dimensions, when the bipartitioning area is , we use additional local structure in the proof and show that . This is at the cusp of being nontrivial in the 2D case, in the sense that any further improvement would yield a subvolume law.
- Received 12 November 2011
DOI:https://doi.org/10.1103/PhysRevB.85.195145
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Published by the American Physical Society