The ground state and the thermodynamics of a spin-1/2 asymmetric diamond Ising--Heisenberg chain are considered. For the
XYZ anisotropic Heisenberg interaction, the exact calculations of the free energy, entropy, heat capacity, magnetization, and magnetic susceptibility are performed using the method of decoration-iteration transformation. In the case of antiferromagnetic interactions (Ising and
XXZ anisotropic Heisenberg ones), the ground state, magnetization process, temperature dependence of the magnetization, magnetic susceptibility, and heat capacity are investigated. The influence of geometric frustration and quantum fluctuations on these characteristics is studied.
This thesis is divided into 4 chapters. The first chapter gives a brief discussion on the
need for the study of Quantum spin systems, and an introduction to Heisenberg Model. In the
second chapter, we start the discussion with Quantum entanglement and then go on to show
the importance of anti ferromagnetic ground state from the view of entanglement. In the third
chapter, we discuss the ways to obtain the ground states of Heisenberg model, both ferromagnet
and antiferromagnet. Then we discuss the effect of magnetic field on the antiferromagnetic
ground states, for a good understanding of magnetic properties in Chapter(4). In the fourth and
the final chapter, we discuss how Bonner Fisher model uses the Bethe ansatz to obtain all the
properties of finite Heisenberg chains. Then we analyze the magnetic properties, like Magnetic
moment and Susceptibility, of Heisenberg antiferromagnets for finite as well as infinite chains.
The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.