Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ground State Entanglement in One Dimensional Translationally Invariant
  Quantum Systems   We examine whether it is possible for one-dimensional
translationally-invariant Hamiltonians to have ground states with a high degree
of entanglement. We present a family of translationally invariant Hamiltonians
{H_n} for the infinite chain. The spectral gap of H_n is Omega(1/poly(n)).
Moreover, for any state in the ground space of H_n and any m, there are regions
of size m with entanglement entropy Omega(min{m,n}). A similar construction
yields translationally-invariant Hamiltonians for finite chains that have
unique ground states exhibiting high entanglement. The area law proven by
Hastings gives a constant upper bound on the entanglement entropy for 1D ground
states that is independent of the size of the region but exponentially
dependent on 1/Delta, where Delta is the spectral gap. This paper provides a
lower bound, showing a family of Hamiltonians for which the entanglement
entropy scales polynomially with 1/Delta. Previously, the best known such bound
was logarithmic in 1/Delta.

24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex