Antiferromagnetic spin-S chains with exactly dimerized ground states

TL;DR

This paper identifies a specific three-body interaction in spin-S chains that guarantees a fully dimerized ground state, generalizing known models and analyzing phase transitions with numerical methods, with implications for real materials.

Contribution

It introduces a generalized model with an exactly dimerized ground state for arbitrary spin S, extending the Majumdar-Ghosh point, and explores phase transitions and physical realizations.

Findings

Exact dimerized ground states for spin-S chains with specific three-body interactions.

Continuous transition between Haldane and dimerized phases with central charge c=3/2 for S=1.

Three-body interactions naturally emerge in strong-coupling Hubbard models.

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.