Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathrm{U(1)}$ and $\mathbb{Z}_2$ spin liquids on the pyrochlore
  lattice   The geometrically frustrated 3D pyrochlore lattice has been long predicted to
host a quantum spin liquid, an intrinsic long-range entangled state with
fractionalized excitations. To date, most proposals for pyrochlore materials
have focused on quantum spin ice, a $\mathrm{U(1)}$ quantum spin liquid whose
only low energy excitations are emergent photons of Maxwell type. In this work,
we explore the possibility of finding pyrochlore quantum spin liquids whose low
energy theories go beyond this standard one. We give a complete classification
of symmetric $\mathrm{U(1)}$ and $\mathbb{Z}_2$ spin liquids on the pyrochlore
lattice within the projective symmetry group framework for fermionic spinons.
We find 18 $\mathrm{U(1)}$ spin liquids and 28 $\mathbb{Z}_2$ spin liquids that
preserve pyrochlore space group symmetry while, upon further imposing time
reversal symmetry, the numbers of classes become 16 and 48, respectively. For
each class, the most general symmetry-allowed spinon mean-field Hamiltonian is
given. Interestingly, we find that several $\mathrm{U(1)}$ spin liquid classes
possess an unusual gapless multi-nodal-line structure ("nodal star") in the
spinon bands, which is protected by the projective actions of the three-fold
rotation and screw symmetries of the pyrochlore space group. Through a simple
model, we study the effect of gauge fluctuations on such a nodal star spin
liquid and propose that the leading terms in the low temperature specific heat
have the scaling form $C/T\sim \sqrt{T}+\sqrt{T}/\ln T$, in contrast to the
form $C/T \sim T^2$ of the standard $\mathrm{U(1)}$ pyrochlore spin liquid with
gapped spinons.

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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: math
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The categories of this paper are: astro-ph
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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: stat
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The categories of this paper are: eess
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The categories of this paper are: physics