Abstract
We study the spectrum of an integrable antiferromagnetic Hamiltonian of the gl(M|N) spin chain of alternating fundamental and dual representations. After extensive numerical analysis, we identify the vacuum and low lying excitations and with this knowledge perform the continuum limit, while keeping a finite gap. All antiferromagnetic gl(n + N|N)spin chains with n, N > 0 are shown to possess in the continuum limit 2n −2 multiplets of massive particles which scatter with gl(n)Gross-Neveu like S-matrices, meaning that their eigenvalues do not depend on N. We argue that the continuum theory is the gl(M|N) Gross-Neveu model, that is the massive deformation of the \( {{s\hat{l}}}{\left( {M\left| N \right.} \right)_1} \) Wess-Zumino-Witten model. As we can see in the example of gl(2 m|1) spin chains, the full particle spectrum is much richer. Our analysis suggests that for a complete characterization of the latter it is not enough to restrict to large volume calculations, as we do in this work.
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Candu, C. The continuum limit of gl(M|N) spin chains. J. High Energ. Phys. 2011, 69 (2011). https://doi.org/10.1007/JHEP07(2011)069
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DOI: https://doi.org/10.1007/JHEP07(2011)069