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arXiv:1112.3403 · Nuclear Physics B

Continuum limit and symmetries of the periodic gℓ(1|1) spin chain

Azat M. Gainutdinov, N. Read, Hubert Saleur

Published Jan 29, 2013• 50 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2013.01.018

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•Jan 1, 2011•6 citations
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.
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.