The work is devoted to the theoretical study of the energy spectrum and magnetic properties of the modified antiferromagnetic spin (1/2, s) diamond chain. This is a frustrated mixed spin system with the unit cells formed by two spin ½ and one spin s>1/2. On the base of extended Lieb theorem we proved the possibility of the appearance of quantum phase transitions mediated by ratio of coupling parameters at arbitrary nonzero value of the spin s for the above model. The results of our exact diagonalization study for some finite chain clusters with s=1 supports this conclusion. We also studied analytically and numerically magnetic properties of Heisenberg –Ising diamond mixed spin chain. The exact energy spectrum of this model is found in analytical form at arbitrary values of model parameters. On the base of this spectrum we studied the field dependence of two-particle correlators for neighbor Ising spins. It was found that at special relation between coupling parameters there is a critical value of external magnetic field for which the above correlator takes zero value (the absence of the correlation between Ising spins). For infinite spin chain model we studied field dependence of specific magnetization by means of classical transfer- matrix method and found intermediate plateau in the low-temperature magnetization profile. According to our calculations, the size of this plateau depends strongly on the relations between coupling parameters of the model. We hope this feature of our model gives new possibilities for the design of new magnetic chemo-sensors.
We consider the open XXZ spin chain with unparallel boundary fields, in the special case in which the Vertex-IRF transform of the K-matrix labelling the boundary field at site 1 is diagonal and invariant under the value of the gauge parameters, the other K-matrix being arbitrary. We discuss here several properties related to this special gauge invariant boundary condition. Such a model can be solved in the Vertex-IRF framework with arbitrary gauge parameters: we can diagonalise the transfer matrix by means of generalised Sklyanin's Separation of Variable (SoV) approach in a family of SoV bases that depend on two arbitrary gauge parameters
α and
β,
β being the so-called dynamical parameter and
α an arbitrary shift of the spectral parameter. We show here that such SoV bases depend actually on
α and
β through the difference
α−β only. Considering the ungauged limit in which
α−β tends to infinity, we show how to compute all elementary building blocks for the correlation functions of this model. We finally show how to compute overlaps between eigenstates of this model and eigenstates of a spin chain sharing the same boundary condition at site
N and in which the gauge invariant boundary condition at site 1 has been changed to a more general one.
The modified spin-wave (M-SW) theory is generalized to the case of arbitrary range interactions. Applying the results of the theory to the system with up to NNN interactions, we have obtained the analytical expressions of thermodynamic quantities at low temperatures and also analyzed the anomalous behavior near the generalized cross-over point. Numerical calculations of the case S = 1/2 have been performed to compare the results with those obtained by the exact diagonalization method. Our numerical results give a fairly good agreement with those of the exact-diagonalization-method.