Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Critical Phenomena, Entanglement Entropy and Hubbard Model in 1d
  with the Boundary Site with a Negative Chemical Potential -p and the Hubbard
  Coupling U Positive   Recently the ground state and some excited states of the half-filled case of
the 1d Hubbard model were discussed for an open chain with L sites. Authors
considered the case when the boundary site has a negative chemical potential -p
and the Hubbard coupling U is positive. They have shown by an analytic method
that when p is larger than the transfer integral some of the ground-state
solutions of the Bethe ansatz equations become complex-valued. They have found
that there is a surface phase transition at some critical value p_c; when p <
p_c all the charge excitations have the gap for this case, while there exists a
massless charge mode when p > p_c. To find whether this surface phase
transition is of the first order or of the second order we have used the
entanglement entropy concept. The entropy and its derivative has a
discontinuity there, so this transition is of the first order.

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The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics