The DMRG method is applied to integrable models of antiferromagnetic spin chains for fundamental and higher representations of SU(2), SU(3), and SU(4). From the low energy spectrum and the entanglement entropy, we compute the central charge and the primary field scaling dimensions. These parameters allow us to identify uniquely the Wess-Zumino-Witten models capturing the low energy sectors of the models we consider.Comment: 14 pages, 8 figures; final version, to appear in Ann. Phy
We use extensive DMRG calculations to show that a classification of SU(n) spin chains with regard to the existence of spinon confinement and hence a Haldane gap obtained previously for valence bond solid models applies to SU(n) Heisenberg chains as well. In particular, we observe spinon confinement due to a next-nearest neighbor interaction in the SU(4) representation 10 chain. PACS numbers: 75.10.Jm, 75.10.Pq, 75.40.Mg, 37.10.Jk Introduction.-The properties of quantum spin chains have been a vital area of research in condensed matter physics. Starting with Bethe's solution of the spin 1 2 Heisenberg model (HM) in 1931 1 , the field quickly evolved and significantly influenced many other areas of physics. In accordance to previous findings by Andrei and Lowenstein 2 , Faddeev and Takhtajan 3 observed in 1981 by consideration of Bethe Ansatz solutions that the elementary excitations of spin chains are spinons carrying spin 1/2. From the identification of the O(3) nonlinear sigma model as the low-energy field theory of antiferromagnetic SU (2) spin chains, Haldane conjectured in 1983 that chains with integer spin possess a gap in the magnetic excitation spectrum, while a topological term renders half-integer spin chains gapless 4 . This, and in particular the gap in the magnetic energy spectrum for integer chains, was confirmed by experiment 5 . An elegant paradigm of the gapped spin 1 chain in terms of a valence bond solid (VBS) model was given by Affleck, Kennedy, Lieb, and Tasaki (AKLT) 7 .
The DMRG method is applied to integrable models of antiferromagnetic spin chains for fundamental and higher representations of SU(2), SU(3), and SU(4). From the low energy spectrum and the entanglement entropy, we compute the central charge and the primary field scaling dimensions. These parameters allow us to identify uniquely the Wess–Zumino–Witten models capturing the low energy sectors of the models we consider.
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