Size-dependent low-energy excitations in an alternating spin-1/spin- ½ antiferromagnetic chain: spin-wave theory and density-matrix renormalization-group studies

Abstract

We study the properties of the ground state and the low-lying excited states of an alternating spin-1 and spin-1/2 antiferromagnetic chain with ferromagnetic next-nearest-neighbor coupling with a variety of methods, namely, spin-wave analysis, density-matrix renormalization-group (DMRG) method, and exact-diagonalization method. The ground state of this model with 2N spins is ferrimagnetic with the total spin S_G=N/2 for all parameter values. In the long chain limit, a gapless excitation is found with characteristics of goldstone mode of the ferromagnetic order with total spin S=S_G-1. The lowest gapped excitation, however, exists in the total spin S=S_G+1 sector. Interestingly, we find that with the increase in ferromagnetic coupling, spin-wave gapped excitation becomes lower than the massless mode for the large wave numbers. Correspondingly, from DMRG analysis we find that the excitation in the total spin S=S_G+1 is lower than that in the total spin S=S_G-1 when the size of the chain is short and the ferromagnetic interaction is large. Characteristics of these excitations are also reflected in the low temperature thermodynamic quantities, where the low-energy properties are strongly affected by the system size and the coupling strength.