Physical Review Letters

Excitation Spectrum of a Dimerized Next-Neighbor Antiferromagnetic Chain

B. Sriram Shastry, Bill Sutherland

Published Sep 28, 1981• 328 citations

Abstract

The excitation spectrum of an antiferromagnetic chain exhibiting the effects of both dimerization and frustration is studied. The method used is based on an exact solution for the doubly degenerate ground state, and views the excitations as propagating defect boundaries between the two exact ground states. These excitations are analogous to "solitons," and can bind into a second type of excitation, analogous to "breathers."

DOI: 10.1103/physrevlett.47.964

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Physical Review Letters

Excitation Spectrum of a Dimerized Next-Neighbor Antiferromagnetic Chain

B. Sriram Shastry, Bill Sutherland

Published Sep 28, 1981• 328 citations

Publisher

Abstract

DOI: 10.1103/physrevlett.47.964

Related papers

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T. Vekua, A. Honecker

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Jan 24, 20060 citations

Starting from the exact result of Majumdar and Ghosh for the dimerized ground state of a Heisenberg linear-chain antiferromagnet with competing next-nearest-neighbor interaction

{\mathit{J}}_{2}

=1/2

{\mathit{J}}_{1}

, it is shown that this state is an exact eigenstate of the same Hamiltonian with couplings extended up to fourth-nearest neighbors, if the relations

{\mathit{J}}_{1}

-2

{\mathit{J}}_{2}

{\mathit{J}}_{3}

=0 and

{\mathit{J}}_{3}

{\mathit{J}}_{4}

hold. Furthermore, it is proved to all orders in perturbation theory that this state is the ground state of this Hamiltonian in a finite interval of values of the parameter \ensuremath{\lambda}==1/2-

{\mathit{j}}_{2}

around \ensuremath{\lambda}=0. The actual extension of this interval is computed numerically for finite chains and is shown to be significant.

(S=0)

and triplet

(S=1)

modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter \ensuremath{\delta} is not too small $(\ensuremath{\delta}>0.1),$ i.e., while the elementary triplets can be treated as localized objects.