The two-dimensional t-J model on the square lattice is studied as a relevant model to capture the essential physics of the high-temperature copper-oxide superconductors. In order to gain understanding of the basic physics of the model, fundamental issues such as the motion of a single hole and the binding of two holes in a quantum antiferromagnet are addressed. A numerical approach is followed, combining a variation calculation with the use of the Green's function Monte Carlo method, applied in this thesis for the first time to study the t-J model in the presence of mobile holes. Important insight is obtained on the effect of a single hole on the antiferromagnetic background and on the occurrence of binding of two holes. It is found that a critical value $(t/J)\sb{c}$ of the parameter t/J of the model exists such that hole binding no longer takes place for $t/J>(t/J)\sb{c},$ with $(t/J)\sb{c}\sim3.7.$ The value that t/J should have in the real material is estimated to be about 3, in order for the model to be relevant to superconductivity. Further research developments are discussed. / Source: Dissertation Abstracts International, Volume: 53-10, Section: B, page: 5271. / Major Professor: Efstratios Manousakis. / Thesis (Ph.D.)--The Florida State University, 1992.

Strongly correlated materials are a class of materials that cannot be properly described by the Density Functional Theory (DFT), which is a single-particle approximation to the original many-body electronic Hamiltonian. These systems contain d or f orbital electrons, i.e., transition metals, actinides, and lanthanides compounds, for which the electron-electron interaction (correlation) effects are too strong to be described by the single-particle approximation of DFT. Therefore, complementary many-body methods have been developed, at the model Hamiltonians level, to describe these strong correlation effects. Dynamical Mean Field Theory (DMFT) and Rotationally Invariant Slave-Boson (RISB) approaches are two successful methods that can capture the correlation effects for a broad interaction strength. However, these many-body methods, as applied to model Hamiltonians, treat the electronic structure of realistic materials in a phenomenological fashion, which only allow to describe their properties qualitatively. Consequently, the combination of DFT and many body methods, e.g., Local Density Approximation augmented by RISB and DMFT (LDA+RISB and LDA+DMFT), have been recently proposed to combine the advantages of both methods into a quantitative tool to analyze strongly correlated systems. In this dissertation, we studied the possible improvements of these approaches, and tested their accuracy on realistic materials. This dissertation is separated into two parts. In the first part, we studied the extension of DMFT and RISB in three directions. First, we extended DMFT framework to investigate the behavior of the domain wall structure in metal-Mott insulator coexistence regime by studying the unstable solution describing the domain wall. We found that this solution, differing qualitatively from both the metallic and the insulating solutions, displays an insulating-like behavior in resistivity while carrying a weak metallic character in its electronic structure. Second, we improved DMFT to describe a Mott insulator containing spin-propagating and chargeless fermionic excitations, spinons. We found the spinon Fermi-liquid, in the Mott insulating phase, is immiscible to the electron Fermi-liquid, in the metallic phase, due to the strong scattering between spinons in a metal. Third, we proposed a new approach within the slave-boson (Gutzwiller) framework that allows to describe both the low energy quasiparticle excitation and the high energy Hubbard excitation, which cannot be captured within the original slave-boson framework. In the second part, we applied LDA+RISB to realistic materials modeling. First, we tested the accuracy of LDA+RISB on predicting the structure of transition metal compounds, CrO, MnO, FeO, CoO, CoS, and CoSe. Our results display remarkable agreements with the experimental observations. Second, we applied LDA+RISB to analyze the nature of the Am-O chemical bonding in the CsAm(CrO_4)_2 crystal. Our results indicate the Am-O bonding has strongly covalent character, and they also address the importance of the correlation effects to describe the experimentally observed electronic structure. In summary, we proposed three extensions within DMFT and RISB framework, which allow to investigate the domain wall structure in metal-Mott insulator coexistence regime, the metal-to-Mott-insulator transition with spinons excitation in the Mott-insulating phase, and the Hubbard excitation within RISB approach. Furthermore, we demonstrated that LDA+RISB is a reliable approximation to the strongly correlated materials by applying it to the transition metal compounds and the Americian chromate compounds. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2017. / July 12, 2017. / Density functional theory, Electronic structure simulations, Many-body methods, Mott transition, Strongly correlated system / Includes bibliographical references. / Vladimir Dobrosavljevic, Professor Directing Dissertation; Naresh S. Dalal, University Representative; Efstratios Manousakis, Committee Member; Luis Balicas, Committee Member; Jorge Piekarewicz, Committee Member.

Quantum computing gives novel way of computing using quantum mechanics, which furthers human knowledge and has exciting applications. Quantum systems with diluted spins such as rare earth ions hosted in single crystal, molecule-based magnets etc. are promising qubits candidates to form the basis of a quantum computer. High sensitivity measurement and coherent control of these spin systems are crucial for their practical usage as qubits. The micro-SQUID (direct-current micrometer-sized Superconducting QUantum Interference Device) is capable to measure magnetization of spin system with high sensitivity. For example, the micro-SQUID technique can measure magnetic moments as small as several thousand μB as shown by the study of [W. Wernsdorfer, Supercond. Sci. Technol. 22, 064013 (2009)]. Here we develop a novel on-chip setup that combines the micro-SQUID sensitivity with microwave excitation. Such setup can be used for electron spin resonance measurements or coherent control of spins utilizing the high sensitivity of micro-SQUID for signal detection. To build the setup, we studied the fabrication process of the micro-SQUID, which is made of weak-linked Josephson junctions. The SQUID as a detector is integrated on the same chip with a shorted coplanar waveguide, so that the microwave pulses can be applied through the waveguide to excite the sample for resonance measurements. The whole device is plasma etched from a thin (∼20nm) niobium film, so that the SQUID can work at in large in-plane magnetic fields of several tesla. In addition, computer simulations are done to find the best design of the waveguide such that the microwave excitation field is sufficiently strong and uniformly applied to the sample. The magnetization curve of Mn₁₂ molecule-based magnet sample is measured to prove the proper working of the micro-SQUID. Electron spin resonance measurement is done on the setup for gadolinium ions diluted in a CaWO₄ single crystal. The measurement shows clear evidence of the resonance signal from the 1st transition of the gadolinium ions' energy levels, which shows the setup is successfully built. Due to the high sensitivity of micro-SQUID and the ability to concentrate microwave energy in small areas of the chip, this setup can detect signals from a small number of spins (10⁷) in a small volume (several μm³). / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2017. / June 28, 2017. / Resonance, SQUID, waveguide / Includes bibliographical references. / Irinel Chiorescu, Professor Directing Dissertation; Naresh Dalal, University Representative; Laura Reina, Committee Member; Pedro Schlottmann, Committee Member; Peng Xiong, Committee Member.

Source: Dissertation Abstracts International, Volume: 41-01, Section: B, page: 0250. / Thesis (Ph.D.)--The Florida State University, 1980.

A new approach to the high-temperature series expansion which is applicable to systems with complicated energy level schemes such as magnetic systems with crystal-field anisotropy of arbitrary strength has been formulated. We compare this approach with the original Green's function formulation of Wand and Lee and discuss the advantage of the present technique. We apply the approach developed here to the spin-one hard-axis Heisenberg ferromagnet and obtain the first four terms in the high-temperature series expansion for the free energy, the magnetic susceptibility, and the specific heat. The formula obtained for the free energy of the spin-one hard-axis ferromagnet also describes spin-one systems with rhombic anisotropy and reduces to the spin-one ferromagnet with an easy-axis anisotropy and to the spin-one simple Heisenberg systems by setting the appropriate matrix elements equal to zero. The method can be extended to treat systems with spin greater than one with general crystal field symmetry. The calculation of higher order terms is rendered tractable using the approach developed here. / Source: Dissertation Abstracts International, Volume: 41-02, Section: B, page: 0612. / Thesis (Ph.D.)--The Florida State University, 1980.

Source: Dissertation Abstracts International, Volume: 41-09, Section: B, page: 3493. / Thesis (Ph.D.)--The Florida State University, 1980.

Fe$\sb3$O$\sb4$ (magnetite) is a ferromagnetic semiconductor while NiO is an antiferromagnetic insulator with a room temperature resistivity at least six orders of magnitude greater than that of Fe$\sb3$O$\sb4.$ Modulated structure films, with equal Fe$\sb3$O$\sb4$ and NiO layer thicknesses, were grown using plasma assisted molecular beam epitaxy to a total film thickness of 3446A, and with modulation wavelengths $\Lambda$ (bilayer thicknesses) ranging from 16A to 1763A. Post growth $\theta$-2$\theta$ x-ray data contain well defined low angle peaks which confirm that the targeted layer thicknesses were accurately achieved. Resistivity has been measured perpendicular to the plane of the film, as a function of modulation wavelength and temperature. A dependence of the resistivity on $\Lambda$ is observed in two sample sets in which the resistivity rapidly increases many orders of magnitude as the modulation wavelength decreases from the bulk $\Lambda\rightarrow\infty$ limit in the vicinity of 600A. This length scale dependent resistivity enhancement of the Fe$\sb3$O$\sb4$/NiO modulated structures cannot be explained by the standard model of interfacial resistance. A qualitative argument is presented for a metal-insulator-metal interfacial charge transfer model which contains both the resistivity enhancement and the observed length scale dependence. / Source: Dissertation Abstracts International, Volume: 57-04, Section: B, page: 2634. / Major Professor: L. R. Testardi. / Thesis (Ph.D.)--The Florida State University, 1996.

Analytical and numerical methods are used to study the stationary properties of equilibrium and metastable phases in scalar field theories and model systems with weak, long-range forces (WLRF) by determining the finite-range scaling (FRS) of the free energy F and its analytic continuation $\tilde F$ into the metastable phase. The scaling properties of d-dimensional $\phi\sp n$ scalar field theories are derived, and two special cases are used to study equilibrium and non-equilibrium critical phenomena in WLRF systems. A criterion of critical equivalence is identified, relating the FRS of WLRF systems to the finite-size scaling of hypercylindrical systems above the upper critical dimension. A method of analytically continuing the equilibrium free energy into the metastable phase is generalized for systems exhibiting multiple metastable phases, and new scaling results for $\tilde F$ are found near classical spinodals, including exact results for $d=1.$ An analytic continuation of the free energy is performed numerically on two hypercylindrical systems and compared to analytic expansions for equivalent field theories. Transfer-matrix (TM) finite-size scaling confirms the critical exponents for $d=1$ WLRF systems. For metastable phases, a constrained-transfer-matrix (CTM) method is applied, in which one obtains a "constrained" free-energy density computed directly from the TM. Monte Carlo simulation is performed to obtain decay rates directly, which are compared with both the CTM results and the analytic continuation using Langer's proportionality relation. / Source: Dissertation Abstracts International, Volume: 56-01, Section: B, page: 0316. / Major Professor: Per Arne Rikvold. / Thesis (Ph.D.)--The Florida State University, 1994.

We numerically investigate the finite-size scaling properties of the superfluid density and of the specific heat of superfluid $\sp4He$ confined in cubic and film geometries by using the $x - y$ model and the Cluster Monte-Carlo method. We show that the superfluid density and the specific heat of $\sp4He$, confined in a cubic geometry, scale with respect to the linear length of the system according to finite-size scaling theory, and we derive the temperature dependence of these quantities in the bulk limit by extrapolating the values of the superfluid density and the specific heat obtained for finite lattices to the values corresponding to a lattice of infinite extent. In the case of the film geometry, $\sp4He$ exhibits a Kosterlitz-Thouless phase transition at the thickness-dependent critical temperature, i.e., close to this temperature superfluid helium behaves effectively two-dimensional. We show that the boundary conditions imposed in the top and bottom layers of the film strongly influence the shape of the universal scaling functions of the superfluid density and the specific heat with respect to the film thickness. We always compare our results to the experiments. / Source: Dissertation Abstracts International, Volume: 56-04, Section: B, page: 2111. / Major Professor: Efstratios Manousakis. / Thesis (Ph.D.)--The Florida State University, 1995.

The numerical calculation of the partition function of the 3d Ising model and the 2d XY model are performed using the newly developed Spectral Density method. The performance and utility of the method are also shown. The finite size scaling of the complex zeros of the partition function is used to estimate the critical exponent $\nu$ for the two models. Good estimates of $\nu$ exist for the 3d Ising model and are found to agree with the estimates calculated here. Recently, there has been debate over whether the XY model has an infinite order phase transition as previously believed or a finite order transition. The critical exponent $\nu$ is sensitive to this question. Unlike a finite order transition, it is impossible to define $\nu$ for an infinite order transition. It is shown that if estimates of $\nu$ are measured for an infinite order transition, the estimates will diverge in the thermodynamic limit. The nature of the XY model's phase transition is explored by finding estimates of $\nu$ and the behavior of the derivatives of the free energy; however, the results are inconclusive. / Source: Dissertation Abstracts International, Volume: 50-08, Section: B, page: 3549. / Major Professor: Dennis W. Duke. / Thesis (Ph.D.)--The Florida State University, 1989.