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.
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.
This thesis is dedicated to the analytical and numerical study of quantum entanglement and nonlocality in strongly correlated quantum spin tube models in connection with various thermodynamic properties and magnetization processes. More specifically, the study builds on the analysis of the behavior of these physical quantities within a particular spinning network that includes competitive interactions and quantum fluctuations known as a three-leg spins ladder or triangular spin tube, due to the periodic boundary conditions imposed on the three spins that form the Heisenberg steps of this network. In systems with this structure described above, magnetization plateaus are formed due to the competition imposed by the geometric frustration that the network imposes on the spins and the applied external field. Such competition is the mechanism that defines the orientation of the magnetic domains that the network will present, which within specific regions of the network parameters space create regions where there is a discontinuous response of local magnetization to external field variations, such regions are known as magnetization plateaus. To evaluate the frustrated spin- ½ Ising-Heisenberg triangular tube consisting of a spin tube formed by triangular unit cells with 3 spins-½ interconnected by Heisenberg couplings between neighboring first spins and the pairs of neighboring first spins belonging to the different cells have their interaction intermediated through classical Ising couplings, an exact analytical procedure, known as a transfer-matrix technique, was used to obtain the analytical solutions for various thermodynamic properties of the model, including magnetization, specific heat and magnetization profiles. These quantities were evaluated as a function of temperature, external magnetic field and the relevant couplings. However, it was necessary to apply a different methodology to obtain thermodynamic measurements for the other model proposed in this thesis: the frustrated spin- ½ Heisenberg triangular tube, which consists of a spin tube with similar structure to the previous one, except that the pairs of the first neighboring spins belonging to the different cells interact through Heisenberg-type quantum connections. In this case, a numerical procedure known as the quantum density matrix renormalization group method, known as DMRG, is used to obtain the ground state diagrams, magnetization processes, and bipartite quantum entanglement of the Heisenberg triangular tubes as a function of the external magnetic field and the relevant couplings. In both models, the magnetization curves exhibit discontinuous magnetization jumps and intermediate plateaus due to discontinuous phase transitions induced by the external field, These transitions are also reflected in the exotic behavior of some thermodynamic quantities of the models, such as the presence of a striking low temperature peak for the specific heat curve and a highlighted magnetocaloric effect.
The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.
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…
The magnetic and thermodynamic properties of spin-1∕2 Heisenberg diamond chains are investigated in three different cases: (a) J1, J2, J3>0 (frustrated), (b) J1, J3<0, J2>0 (frustrated), and (c) J1, J2>0, J3<0 (nonfrustrated), where the bond coupling Ji(i=1,2,3)>0 stands for an antiferromagnetic (AF) interaction, and <0 for a ferromagnetic (F) interaction. The density-matrix renormalization-group (DMRG) technique is invoked to study the properties of the system in the ground state, while the transfer-matrix renormalization-group (TMRG) technique is applied to explore the thermodynamic properties. The local magnetic moments, spin-correlation functions, and static structure factors are discussed in the ground state for the three cases. It is shown that the static structure factor S(q) shows peaks at wave vectors $q=a\ensuremath{\pi}∕3$ (a=0,1,2,3,4,5) for different couplings in a zero magnetic field, which, however, in the magnetic fields where the magnetization plateau with m=1∕6 pertains, exhibits the peaks only at q=0, $2\ensuremath{\pi}∕3$, and $4\ensuremath{\pi}∕3$, which are found to be couplings independent. The DMRG results of the zero-field static structure factor can be nicely fitted by a linear superposition of six modes, where two fitting equations are proposed. It is observed that the six modes are closely related to the low-lying excitations of the system. At finite temperatures, the magnetization, susceptibility, and specific heat show various behaviors for different couplings. The double-peak structures of the susceptibility, and specific heat against temperature are obtained, where the peak positions and heights are found to depend on the competition of the couplings. It is also uncovered that the XXZ anisotropy of F and AF couplings leads the system of case (c) to display quite different behaviors. In addition, the experimental data of the susceptibility, specific heat, and magnetization for the compound Cu3(CO3)2(OH)2 are fairly compared with our TMRG results.
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.
Abstract In the last two decades, magnetic, thermodynamic properties and bipartite thermal entanglement in diamond spin clusters and chains have been studied. Such spin structures are presented in various compounds. The ions of Cu2+ in the natural mineral azurite are arranged in a diamond spin chain. There are no studies of the entanglement behaviour during the quantum evolution of such systems. Herein, we consider the evolution of entanglement in the diamond spin-1/2 cluster. This cluster consists of two central spins described by the anisotropic Heisenberg model, which interact with two side spins via Ising interaction. The influence of the interaction coupling with side spins on the entanglement of central spins is investigated. It is shown that choosing the value of this coupling allows us to control the behaviour of entanglement between central spins. As a result, we find conditions for achieving the maximal values of entanglement. In addition, the entanglement behaviour between the side spins, central and side spins, and between a certain spin and the rest of the system is studied. In these cases, the conditions for achieving maximal entanglement are also obtained.