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.

Phononic and magnetic excitations in the quasi-one-dimensional Heisenberg antiferromagnet KCuF3

“…(i) Many theoretical and experimental investigations have been directed towards the spectroscopic investigations of the spinon continuum in the 1D spin-1/2 systems [50][51][52][53]. The multi-spinon excitation spectrum is observed Raman shift, cm -1 in both low-and high-temperature phases of KCuF 3 in neutron scattering experiments [48,49,54] and was compared to the Müller ansatz [55], an analytic expressions for the two-spinon contribution of the Bethe ansatz solutions [56].…”

Complexity and quenches in models with three and four spin interactions

“…This will be used extensively in the paper, and we first recall their main results. More details can be found in [28,29]. The model Hamiltonian is given by…”

“…In the first branch, E k,1 is negative, and in the second branch, E k,2 is positive for any k. This domain is denoted by I in the phase diagram and is referred to as the ferrimagnetic phase, as can be gleaned from the ground state magnetisation per cell in the thermodynamic limit given by [28,29]…”

“…The purpose of the present paper is to go beyond the physics of nearest neighbour interactions and study these information theoretic quantities in spin models in the presence of three and four spin interactions. Fortunately, an exactly solv-able model with such interactions is known, and was discussed in [27] (see also [28,29]). Here, we study this model with some specific simplifying choice of parameters (that nonetheless preserves a rich phase structure), and show that there are some remarkable differences (as well as similarities) in the behaviour of information theoretic quantities when short range interactions are added to the NN one.…”

Complexity and quenches in models with three and four spin interactions

“…The purpose of the present paper is to go beyond the physics of NN interactions and study these information theoretic quantities in spin models in the presence of three and four spin interactions. Fortunately, an exactly solvable model with such interactions is known, and was discussed in [27] (see also [28,29]). Here, we study this model with some specific simplifying choice of parameters (that nonetheless preserves a rich phase structure), and…”