Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: U(1) spin liquids and valence bond solids in a large-N three-dimensional
  Heisenberg model   We study possible quantum ground states of the Sp(N) generalized Heisenberg
model on a cubic lattice with nearest-neighbor and next-nearest-neighbor
exchange interactions. The phase diagram is obtained in the large-N limit and
fluctuation effects are considered via appropriate gauge theories. In
particular, we find three U(1) spin liquid phases with different short-range
magnetic correlations. These phases are characterized by deconfined gapped
spinons, gapped monopoles, and gapless ``photons''. As N becomes smaller, a
confinement transition from these phases to valence bond solids (VBS) may
occur. This transition is studied by using duality and analyzing the resulting
theory of monopoles coupled to a non-compact dual gauge field; the condensation
of the monopoles leads to VBS phases. We determine the resulting VBS phases
emerging from two of the three spin liquid states. On the other hand, the spin
liquid state near J_1 \approx J_2 appears to be more stable against monopole
condensation and could be a promising candidate for a spin liquid state in real
systems.

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The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg