Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Area law in one dimension: Degenerate ground states and Renyi
  entanglement entropy   An area law is proved for the Renyi entanglement entropy of possibly
degenerate ground states in one-dimensional gapped quantum systems. Suppose in
a chain of $n$ spins the ground states of a local Hamiltonian with energy gap
$\epsilon$ are constant-fold degenerate. Then, the Renyi entanglement entropy
$R_\alpha(0<\alpha<1)$ of any ground state across any cut is upper bounded by
$\tilde O(\alpha^{-3}/\epsilon)$, and any ground state can be well approximated
by a matrix product state of subpolynomial bond dimension $2^{\tilde
O(\epsilon^{-1/4}\log^{3/4}n)}$.

33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an