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.
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 thesis started with a short introduction about my research work and discussed about the systems I worked on. Later, it discussed about the experimental techniques that I have learned during the course of my work. This chapter includes the experimental approaches that I have used in sample preparation, characterization and measurements that I performed on my samples. In third chapter, I introduced about my first research work i.e. experimental quantification of entanglement in CN using magnetic susceptibility and heat capacity. In the fourth chapter, I briefly discussed about the magnetic field and temperature dependence of entanglement estimated using heat capacity. A good agreement with the theoretical predictions of our experimental results was also discussed. The fifth chapter consists of experimental study of quantum discord in CN quantified using magnetic susceptibility and heat capacity. In this chapter also I have discussed that our experimental results exhibits good correspondence with theoretical predictions and earlier reported results. In the sixth and last chapter of my thesis, I have discussed an experimental study we performed to investigate the magnetic properties of NiCr2O4 nanoparticles. Our experimental results have shown development of 2D spin-glass like phase in the nanoparticles of NiCr2O4. The parameter values we obtained by fitting the experimental data with the existing theoretical model for spin-glasses matches well with the reported values.
Spins models, despite their simplicity, are known to describe with great precision physical properties of the materials. Of particular interest are the one-dimensional models that present an exact analytical solution, which can be obtained by the transfer matrix method and the decoration-iteration transformation technique. In this thesis, we studied a spin-electron model and two Ising-Heisenberg spin models, where all models are exactly soluble. The first model we investigate concerns a spin-electron diamond chain with Ising spins located on the local sites and mobile electrons dislocated in the interstitial sites under the external magnetic field action. We analyzed the ground states and the correlation between the spins. We show that thermal fluctuations can lead to the emergence of quantum entanglement above the unfrustrated ground states. We also analyze this same model but for different Landé g-factors. We investigated the phase diagrams at zero temperature. We also analyze the magnetization and we show that the magnetic field can cause the emergence of quantum entanglement in some conditions above the non-entanglement ground states. In this same context, we studied the Ising-XYZ diamond model of spin-1/2, with interaction between the second neighbours of the nodal Ising spins, and an external magnetic field applied to the z-axis. We investigate the phase diagram at zero temperature and the quantum entanglement. We notice that the bipartite entanglement between the pairs of Heisenberg interstitial spins in the natural mineral azurite is insensitive to the external magnetic field applied up to approximately 30 K. The third model we studied is a classical-quantum chain consisting of regularly alternating Ising and Heisenberg spins and with two different local anisotropy axes, subject to an applied external magnetic field. We studied the ground states, the magnetization and the susceptibility. It is evidenced that the investigated spin model reproduces magnetic characteristics of the heterobimetallic coordination compound Dy(NO)3(DMSO)2Cu(opba)(DMSO)2. In this thesis we show that the exact soluble spin models can describe with good precision a class of real magnetic materials, which can present interesting magnetic and thermodynamic properties, and quantum entanglement.
Building on the fundamentals introduced in part I, we employ the Bethe ansatz to study some ground-state properties (energy, magnetization, susceptibility) of the one-dimensional s=1/2 Heisenberg antiferromagnet in zero and nonzero magnetic field. The 2-spinon triplet and singlet excitations from the zero-field ground state are discussed in detail, and their energies are calculated for finite and infinite chains. Procedures for the numerical calculation of real and complex solutions of the Bethe ansatz equations are discussed and applied. The paper is designed as a tutorial for beginning graduate students. It includes 10 problems for further study.
Entanglement, magnetization, and magnetic susceptibility for 1D antiferromagnetic spin 1 and spin 23 Heisenberg XXX model with Dzyaloshinskii–Moriya interaction, single-ion anisotropy, and external magnetic field on the finite chain are obtained.
By means of the density matrix renormalization group (DMRG) method, the magnetic properties of the J-J-J′ quantum Heisenberg chains with spin S=1/2, 1, 3/2 and 2 in the ground states are investigated in the presence of a magnetic field. Two different cases are considered: (a) when J is antiferromagnetic and J′ is ferromagnetic (i.e. the AF-AF-F chain), the system is a ferrimagnet. The plateaus of the magnetization are observed. It is found that the width of the plateaus decreases with increasing the ferromagnetic coupling, and disappears when passes over a critical value. The saturated field is observed to be independent of the ferromagnetic coupling; (b) when J is ferromagnetic and J′ is antiferromagnetic (i.e. the F-F-AF chain), the system becomes an antiferromagnet. The plateaus of the magnetization are also seen. The width of the plateaus decreases with decreasing the antiferromagnetic coupling, and disappears when $J^{\prime}/J $ passes over a critical value. Though the ground state properties are quite different, the magnetization plateaus in both cases tend to disappear when the ferromagnetic coupling becomes more dominant. Besides, no fundamental difference between the systems with spin half-integer and integer has been found.
In this dissertation we present the results of a theoretical investigation of spin models on two-dimensional and quasi one-dimensional lattices, all unified under the concept of quantum frustrated antiferromagnetism, and all discussing various aspects of the antiferromagnetic Heisenberg model on the kagomé lattice. In the Introduction (Chapter 1), we discuss at some length such concepts as frustration and superexchange, among others, which are of common relevance in the rest of the chapters. In Chapter 2, we study the effect of Dzyaloshinskii--Moriya (DM) interactions on the zero-temperature magnetic susceptibility of systems whose low energy can be described by short-range valence bond states. Our work shows that this treatment is consistent with the experimentally observed non-vanishing susceptibility -- in the specified temperature limit -- of the spin-1/2 kagomé antiferromagnetic compound ZnCu3(OH)6Cl2, also known as herbertsmithite. Although the objective of this work is explaining the aforementioned characteristic of the experimental system, our methods are more general and we apply them to the checkerboard and Shastry-Sutherland lattices as well. In Chapter 3, we discuss our findings in the study of ghost-mediated domain wall interactions in the diamondback ladder. These domain walls are the the spin excitations -- the kinks and the antikinks -- separating the ground states along one chain of the ladder. While as individual entities an antikink is energy costly and a kink energy free, our study finds that both interact via the ghosts that they produce in the opposite side of the ladder from where they are located. Through the study of these ghosts, we find that domain walls proliferate in the system above a critical value of the system's coupling constants. It is this proliferation that makes their treatment as free, non-interacting particles impossible, so we study here their interactions both quantitatively and qualitatively, in a region where the latter are yet not very strong, namely below the critical point. Based on the calculated two-body interaction potential, domain walls interact attractively (repulsively) when separated at even (odd) distances, with a strength that decays as 1/sp, where s is their separation and p<1. We also consider higher-order interactions. In the last chapter, Chapter 4, we present our study of the spin-1 kagomé Heisenberg antiferromagnet. Our approach is to first consider an SU(2)-symmetric parent Hamiltonian with known ground states on the S=1 kagomé lattice, in which nearest-neighbor Heisenberg interactions are already present. We then enhance these interactions by an additional Heisenberg term added perturbatively in order to move the system closer to a pure Heisenberg antiferromagnet. The results of this enhancement is obtaining a description of the system in terms of an effective Hamiltonian, namely a transverse field Ising AF on the triangular lattice. Based on the particular values of this effective Hamiltonian, our system is found to be in the order-by-disorder phase.