Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cross-over from an incommensurate singlet spiral state with a
  vanishingly small spin-gap to a valence bond solid state in dimerized
  frustrated ferromagnetic spin-chains   Motivated by the magnetic properties of the spin-chain compounds
LiCuSbO$_4$$\equiv$LiSbCuO$_4$ and Rb$_2$Cu$_2$Mo$_3$O$_{12}$, we study the
ground state of the Heisenberg chain with dimerized nearest-neighbor
ferromagnetic (FM)($J_1, J_1^\prime<0$) and next-nearest-neighbor
antiferromagnetic ($J_2>0$) couplings. Using the density-matrix renormalization
group technique and spin-wave theory we find a first-order transition between a
fully-polarized FM and an incommensurate spiral state at
$2\alpha=\beta/(1+\beta)$, where $\alpha$ is the frustration ratio $J_2/|J_1|$
and $\beta$ the degree of dimerization $J_1^\prime/J_1$.In the singlet spiral
state the spin-gap is vanishingly small in the vicinity of the FM transition,
corresponding to a situation of LiCuSbO$_4$. For larger $\alpha$, corresponding
to Rb$_2$Cu$_2$Mo$_3$O$_{12}$, and smaller $\beta$ there is a crossover from
this frustration induced incommensurate state to an
Affleck-Lieb-Kennedy-Tasaki-type valence bond solid state with substantial
spin-gaps.

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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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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