Antiferromagnetic spin-S chains with exactly dimerized ground states
Abstract
We show that spin S Heisenberg spin chains with an additional three-body interaction of the form (S_{i-1}S_{i})(S_{i}S_{i+1})+h.c. possess fully dimerized ground states if the ratio of the three-body interaction to the bilinear one is equal to 1/(4S(S+1)-2). This result generalizes the Majumdar-Ghosh point of the J_1-J_2 chain, to which the present model reduces for S=1/2. For S=1, we use the density matrix renormalization group method (DMRG) to show that the transition between the Haldane and the dimerized phases is continuous with central charge c=3/2. Finally, we show that such a three-body interaction appears naturally in a strong-coupling expansion of the Hubbard model, and we discuss the consequences for the dimerization of actual antiferromagnetic chains.
Cite
@article{arxiv.1110.3394,
title = {Antiferromagnetic spin-S chains with exactly dimerized ground states},
author = {Frédéric Michaud and François Vernay and Salvatore R. Manmana and Frédéric Mila},
journal= {arXiv preprint arXiv:1110.3394},
year = {2012}
}
Comments
8 pages, 8 figures