Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correlation Length versus Gap in Frustration-Free Systems   Hastings established exponential decay of correlations for ground states of
gapped quantum many-body systems. A ground state of a (geometrically) local
Hamiltonian with spectral gap $\epsilon$ has correlation length $\xi$ upper
bounded as $\xi=O(1/\epsilon)$. In general this bound cannot be improved. Here
we study the scaling of the correlation length as a function of the spectral
gap in frustration-free local Hamiltonians, and we prove a tight bound
$\xi=O(1/\sqrt\epsilon)$ in this setting. This highlights a fundamental
difference between frustration-free and frustrated systems near criticality.
The result is obtained using an improved version of the combinatorial proof of
correlation decay due to Aharonov, Arad, Vazirani, and Landau.

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The categories of this paper are: cs
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph