Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A gapless charge mode induced by the boundary states in the half-filled
  Hubbard open-chain   We discuss the ground state and some excited states of the half-filled
Hubbard model defined on an open chain with L sites, where only one of the
boundary sites has a different value of chemical potential. We consider the
case when the boundary site has a negative chemical potential -p and the
Hubbard coupling U is positive. By an analytic method we show that when p is
larger than the transfer integral some of the ground-state solutions of the
Bethe ansatz equations become complex-valued. It follows 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 the half-filled band, while there exists a
massless charge mode when p>p_c.

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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom