Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Area Law for One Dimensional Quantum Systems   We prove an area law for the entanglement entropy in gapped one dimensional
quantum systems. The bound on the entropy grows surprisingly rapidly with the
correlation length; we discuss this in terms of properties of quantum expanders
and present a conjecture on completely positive maps which may provide an
alternate way of arriving at an area law. We also show that, for gapped, local
systems, the bound on Von Neumann entropy implies a bound on R\'{e}nyi entropy
for sufficiently large $\alpha<1$ and implies the ability to approximate the
ground state by a matrix product state.

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The categories of this paper are: cs
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: econ
28
The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys