Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective Spin Models for Spin-Phonon Chains by Flow Equations   We investigate the anti-adiabatic limit of an anti-ferromagnetic S=1/2
Heisenberg chain coupled to Einstein phonons. The flow equation method is used
to decouple the spin and the phonon part of the Hamiltonian. In the effective
spin model long range spin-spin interactions are generated. We determine the
phase transition from a gapless state to a gapped (dimerised) phase, which
occurs at a non-zero value of the spin-phonon coupling. In the effective phonon
sector a phonon hardening is observed.

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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: econ