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.
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.
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.
Entanglement has been extensively studied from the perspective of Quantum Information Processing for the last decade and various measures of entanglement, to quantify it are now available. Experimentally also it has been possible to measure entanglement in pure state, mostly in optics. However, in recent years there has been significant development in Quantum Condensed Matter systems, especially spin chains, where extraction of entanglement has been made possible through macroscopic witness operators like magnetic susceptibility. In this work, we have studied the magnetic properties of some spin chains, where the exchange interaction can be tuned by preparation technique and we have extracted a magnetic field and temperature dependence of entanglement from susceptibility and magnetization data taken at various temperatures and fields. The spin chains considered here fall in two categories, first one is an alternating dimer model and the second is an infinite spin chain. We have given the experimental plots of entanglement as a function of temperature and magnetic fields and compared them with the theoretical plots.
Well-known theories like Edwards-Anderson and Sherrington-Kirkpatrick models together with some important experimental results for spin glass are introduced in chapter 1. However, there is no single model, capable of explaining all the experimental results obtained from the spin glass materials. We use the theory of quantum entanglement (concurrence) to explore the quantum correlations of a spin glass. Quantum entanglement is a useful physical resource for quantum information and communication. In chapter 2, we discuss how information is encoded and measured. The applications of quantum information in algorithms are also mentioned. As quantum information science is built upon the foundation of quantum mechanics, two important aspects of this area: Einstein, Podolsky and Rosen (EPR) gedanken experiment and the Bell's inequality are introduced in chapter 3. In chapter 4, we discuss the idea of density operator, together with the use of trace and partial trace, to describe the state of the composite system. In chapter 5, a short introduction is made on the various entanglement measures. In chapter 6, the analytical calculations of the concurrence for a 3- and 4-qubit XX model are presented. The plots of concurrence with different means and standard deviations for the 3- and 4-qubit are also presented and analyzed. The concurrence of a 2-qubit system coupled to a spin glass bath of n = 2 to 4 qubits is studied in chapter 7. With an initial separable state, the 2-qubit system reached a steady state in concurrence through time evolution when it is coupled to a quantum spin glass environment. The result is general and the behavior of the concurrence is believed to be similar for n > 4. The quantum discord is used for analyzing the XX model and presented in chapter 8. In addition, the concurrence and discord for the next nearest neighbour interaction have been plotted for 3- and 4-qubit. In chapter 9, the concurrence of the probes that are attached to a spin glass is investigated by varying the external applied magnetic field and the J coupling. By using the quantum dots (qubits) as the probe, it is possible to distinguish a spin glass from a non-spin glass with the different signatures (drop and spike) in the concurrence between the probes. The derived entanglement witness for susceptibility and specific heat capacity are used to distinguish an entangled region from an unentangled region for two different spin glass alloys: LiHoxY1-xF4 and CuxMn in chapter 10. In chapter 11, the entanglement properties of the XXZ Heisenberg (with Dzyaloshinskii-Moriya interaction) and Ising transverse field spin glass models are examined with the use of concurrence for N qubits at one-dimensional level. The concurrence for both models are obtained by using the Kadanoff''s renormalization group (RG) approach. By following the RG fl ow, a first-order and second-order phase transitions are observed by varying the standard deviation of the renormalized couplings. This thesis ends with a conclusion in chapter 12 with suggestions for future research.
This thesis consists of six chapters. The first chapter gives an introduction to the field of low-dimensional magnetic and electronic systems and relevant numerical techniques. The recent developments in molecular magnets are highlighted. The numerical techniques are reviewed along with their advantages and disadvantages from the present perspective. Study of entanglement of a system can give a great insight into the system. At the last part of this chapter a general overview is given regarding entanglement, its measures and its significance in studying many-body systems.
Chapter 2 deals with the technique that has been developed by us for the full symmetry adaptation of non-relativistic Hamiltonians. It is advantageous both computationally and physically/chemically to exploit both spin and spatial symmetries of a system. It has been a long-standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of a point group, particularly for non-Abelian point groups. A very general technique is discussed in this chapter which is a hybrid method based on valence-bond basis and the basis of the z-component of the total spin. This technique is not only applicable to a system with arbitrary site spins and belonging to any point group symmetry, it is also quite easy to implement computationally. To demonstrate the power of the method, it is applied to the molecular magnetic system, Cu6Fe8, with cubic symmetry.
In chapter 3, the extension of the previous hybrid technique to electronic systems is discussed. The power of the method is illustrated by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and is in the largest non-Abelian point group. All the eigenstates of the model are obtained using our technique.
Chapter 4 deals with the thermodynamic properties of an important class of single-chain magnets (SCMs). This class of SCMs has alternate isotropic spin-1/2 units and anisotropic high spin units with the anisotropy axes being non-collinear. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. A transfer matrix (TM) method is developed to study statistical behavior of this class of SCMs. For the first time, it is also discussed in detail that how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. This technique is applied to a real helical chain magnet, which has been studied experimentally.
In the fifth chapter a bipartite entanglement entropy of finite systems is studied using exact diagonalization techniques to examine how the entanglement changes in the presence of long-range interactions. The PariserParrPople model with long-range interactions is used for this…
A new experimental realization of heat capacity as an entanglement witness is reported. Entanglement properties of a low–dimensional quantum spin system are investigated by heat capacity measurements performed down to very low temperatures (400 mK), for various applied magnetic field values. The experimentally extracted results for the value of heat capacity at zero field matches perfectly with the theoretical estimates of entanglement from model Hamiltonians. The studied sample is a spin half antiferromagnetic system that shows a clear signature of quantum phase transition at very low temperatures when the heat capacity is varied as a function of fields at a fixed temperature. The variation of entanglement as a function of field is then explored in the vicinity of the quantum phase transition to capture the sudden loss of entanglement.
This thesis studies four related projects: tuning entanglement for spin systems, de-coherence and dynamics of entanglement, entanglement as measure of electron correlation in chemical systems and quantum algorithms to search for global minima. Chapter 1 presents a general introduction and the motivation for these research areas. It is composed of a brief review of the history and the future of modern computers and the state-of-art areas in quantum computation and information. Chapter 2 will be dedicated to introducing the concept of entanglement, its importance, quantification and applications. Then in Chapter 3, the properties of a set of localized spins, which are coupled to an external magnetic field through exchange interaction, are investigated. It is shown that entanglement can be controlled and tuned by varying the anisotropy parameter in the Hamiltonian, and by introducing impurities into the systems. Furthermore, the scheme for amplifying the internal entanglement by external interaction is also studied. In Chapter 4, the applications of the entanglement concept for de-coherence and dynamics is considered. In particular, the dynamics of entanglement for one-dimensional spin systems, which are coupled through nearest neighbor exchange interaction and subject to an external time-dependent magnetic field, is investigated. Using the two-site density matrix, the time-dependent entanglement of formation between nearest neighbor qubits is calculated. It is found that the entanglement can be localized between nearest neighbor qubits for certain values of the external time-dependent magnetic field. In quantum chemistry calculations, the correlation energy is defined as the difference between the Hartree-Fock limit energy and the exact solution of the non-relativistic Schrödinger equation. In Chapter 5, the application of entanglement as an alternative measure of the electron correlation in quantum chemistry calculations is proposed. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics. Finally, Chapter 6 presents the latest research results in developing quantum algorithms for searching the global minima. In this Chapter, the modified Grover’s quantum algorithm using modest numbers of quantum bits to find a global minimum for real problems is demonstrated.