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String Hypothesis for Spin Chains: A Particle/Hole Democracy

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Abstract

This paper is devoted to integrable \({{\mathfrak{g}\mathfrak{l} (\mathfrak{n} | \mathfrak{m})}}\) spin chains, which allow for formulation of the string hypothesis. Considering the thermodynamic limit of such spin chains, we derive linear functional equations that symmetrically treat holes and particles. The functional equations naturally organize different types of excitations into a pattern equivalent to the one of Y-system, and, not surprisingly, the Y-system can be easily derived from the functional equations. The Y-system is known to contain most of the information about the symmetry of the model, therefore we map the symmetry knowledge directly to the description of string excitations. Our analysis is applicable for highest weight representations which for some choice of the Kac-Dynkin diagram have only one nonzero Dynkin label. This generalizes known results for the AdS/CFT spectral problem and for the Hubbard model.

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  1. Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA

    Dmytro Volin

  2. Bogolyubov Institute for Theoretical Physics, 14b Metrolohichna Str., Kiev, 03143, Ukraine

    Dmytro Volin

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Volin, D. String Hypothesis for Spin Chains: A Particle/Hole Democracy. Lett Math Phys 102, 1–29 (2012). https://doi.org/10.1007/s11005-012-0570-9

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