Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomalies and unnatural stability of multi-component Luttinger liquids
  in $\mathbb{Z}_n\times\mathbb{Z}_n$ spin chains   We study translationally invariant spin chains where each unit cell contains
an $n$-state projective representation of a $\mathbb{Z}_n\times\mathbb{Z}_n$
internal symmetry, generalizing the spin-1/2 XYZ chain. Such spin chains
possess a generalized Lieb-Schulz-Mattis (LSM) constraint, and we demonstrate
that certain $(n-1)$-component Luttinger liquids possess the correct anomalies
to satisfy these LSM constraints. For $n = 3$, using both numerical and
analytical approaches, we find that such spin chains with nearest-neighbor
interactions appear to be gapless for a wide range of microscopic parameters
and described by a two-component conformally invariant Luttinger liquid. This
implies the emergence of $n-1$ conserved $U(1)$ charges from only discrete
microscopic symmetries. Remarkably, the system remains gapless for an
unnaturally large parameter regime despite the apparent existence of
symmetry-allowed relevant operators in the field theory. This suggests that
either these spin chains have hidden conserved quantities not previously
identified, or the parameters of the field theory are simply unnatural due to
frustration effects of the lattice Hamiltonian. We argue that similar features
are expected to occur in: (1) $\mathbb{Z}_n\times\mathbb{Z}_n$ symmetric chains
for $n$ odd, and (2) $\mathbb{S}_n\times\mathbb{Z}_n$ symmetric chains for all
$n > 2$. Finally, we suggest the possibility of a lower bound growing with $n$
on the minimum central charge of field theories that possess such LSM
anomalies.

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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc