Elementary excitations and thermodynamics of zig-zag spin ladders with alternating nearest neighbor exchange interactions

Abstract

The one-dimensional spin-1/2 model, in which the alternation of the exchange interactions between neighboring spins is accompanied by the next-nearest neighbor (NNN) spin exchange (zig-zag spin ladder with the alternation) is studied. Thermodynamic characteristics of the considered quantum spin chain are obtained in the mean-field like approximation. Depending on the strength of the NNN interactions, the model manifests either the spin-gapped behavior of low-lying excitations at low magnetic fields, or the ferrimagnetic ordering in the ground state with gapless low-lying excitations. The system undergoes second order or first order quantum phase transitions, governed by the external magnetic field, NNN coupling strength, and the degree of the alternation. Hence, NNN spin–spin interactions in a dimerized quantum spin chain can produce a spontaneous magnetization. On the other hand, for quantum spin chains with a spontaneous magnetization, caused by NNN spin–spin couplings, the alternation of nearest-neighbor (NN) exchange interactions can be the reason for destroying of that magnetization and the onset of a spin gap for low-lying excitations. Alternating NN interactions produce a spin gap between two branches of low-energy excitations, and the NNN interactions yield asymmetry of dispersion laws of those excitations, with possible minima, corresponding to incommensurate structures in the spin chain.