Eur. Phys. J. B 56, 7-14 (2007)
https://doi.org/10.1140/epjb/e2007-00082-x

Modified spin-wave theory for the S = 1 frustrated antiferromagnetic Heisenberg chain

¹ Dept. de Fisica, ICEx, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Pampulha, 31270-901 Belo Horizonte, Brazil
² Centro Federal de Educação Tecnológica de Minas Gerais, 31270-901 Belo Horizonte, Brazil

Corresponding author: ^a gmrocha@fisica.ufmg.br

Received: 5 October 2006
Revised: 20 December 2006
Published online: 21 March 2007

Abstract

We study the one-dimensional isotropic spin-1 Heisenberg magnet with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions by using the modified spin wave theory (MSWT). The ground state energy and the singlet-triplet energy gap are obtained for several values of j, defined as the ratio of the nnn interaction constant to the nn one. We also compare two different ways of implementing the MSWT currently found in the literature, and show that, despite the remarkable differences between the equations to be solved in each procedure, the results given by both are equivalent, except for the predicted value of the j_max, the maximum value of j accessible in each treatment. Here, we suggest that j_max is related to the disorder point of the first kind. Our results show that the ground state and the gap energies increase with j, for j ≤j_max, in accordance to previous numerical results.