Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical study of incommensurate and decoupled phases of spin-1/2
  chains with isotropic exchange J1, J2 between first and second neighbors   The spin-1/2 chain with isotropic exchange J1, J2 > 0 between first and
second neighbors is frustrated for either sign of J1 and has a singlet ground
state (GS) for J1/J2 $\ge - 4$. Its rich quantum phase diagram supports
gapless, gapped, commensurate (C), incommensurate (IC) and other phases.
Critical points J1/J2 are evaluated using exact diagonalization (ED) and
density matrix renormalization group (DMRG) calculations. The wave vector $q_G$
of spin correlations is related to GS degeneracy and obtained as the peak of
the spin structure factor $S(q)$. Variable $q_G$ indicates IC phases in two
$J1/J2$ intervals, [ -4, -1.24] and [0.44, 2], and a C-IC point at J1/J2 = 2.
The decoupled C phase in [-1.24, 0.44] has constant $q_G = {\pi}/2$,
nondegenerate GS, and a lowest triplet state with broken spin density on
sublattices of odd and even numbered sites. The lowest triplet and singlet
excitations, $E_m$ and $E_{\sigma}$, are degenerate in finite systems at
specific frustration $J1/J2$. Level crossing extrapolates in the thermodynamic
limit to the same critical points as $q_G$. The $S(q)$ peak diverges at $q_G =
{\pi}$ in the gapless phase with $J1/J2 > 4.148$ and quasi-long-range order
(QLRO({$\pi$})). $S(q)$ diverges at $\pm {\pi}/2$ in the decoupled phase with
QLRO({$\pi$}/2), but is finite in gapped phases with finite range correlations.
Numerical results and field theory agree at small $J2/J1$ but disagree for the
decoupled phase with weak exchange $J1$ between sublattices. Two related models
are summarized: one has an exact gapless decoupled phase with QLRO({$\pi$}/2)
and no IC phases; the other has a single IC phase without a decoupled phase in
between.

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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cs