Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Phase Transition between Z2 spin liquid and columnar Valence
  Bond Crystals on a Triangular lattice   We study the quantum phase transition between the $Z_2$ spin liquid and
valence bond solid (VBS) orders on a triangular lattice. With a fully isotropic
triangular lattice, the transition from a columnar or resonating-plaquette VBS
order can be either first order or there could be two transitions with an
intermediate phase. If the transition splits into two, then the $Z_2$ spin
liquid will first experience a first order $q=3$ Potts transition to a new
nematic $Z_2$ spin liquid that breaks the $2\pi/3$ lattice rotation symmetry
(but retain translation symmetry unlike the VBS states). The second transition
will then take this new nematic $Z_2$ spin liquid to a columnar or
resonating-plaquette VBS state through a second order $3d$ XY$^*$ transition.
On a distorted triangular lattice, the degeneracy between some of the different
columnar VBS orders is lifted, and the phase transition can reduce to a single
$3d$ XY$^*$ transition.

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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
9
The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int