On the Properties of Some Strongly Correlated Systems - Analytical and Numerical Studies

Sammanfattning: This thesis is dedicated to analytical and numerical studiesof a few models of strongly correlated systems and thedevelopment of techniques for such studies. The common name"strongly correlated" refers to systems in which theinteractions (correlations) between the constituent particleslead to nontrivial properties, such as various types ofmagnetism, superconductivity, and exotic phases. The thesisbegins with a three-part introductory review and ends withresearch results, presented in the form of scientificarticles.In the first part of the thesis the application of meanfield theory to models of magnetic multilayer systems isdiscussed. Magnetic multilayers are widely used as a medium formagnetooptical recording. The technologically importantproperties of such multilayers are high magnetic anisotropy anda compensation temperature (at which the magnetizations of thedifferent layers cancel each other and the net magnetic momentvanishes) close to room temperature. It is thus beneficial tohave a simple theoretical model, allowing to predict the netmagnetization and compensation temperature of a multilayer,depending on the composition and thickness of the componentlayers. Such a model, featuring long-range interactions betweenthemagnetic layers, has been developed and studied, using meanfield theory. A satisfactory agreement with experiment wasobtained.The second part of the thesis is devoted to possibleenhancements of an experimental technique, known as scanningtunneling microscopy (STM). In this technique a sharp (ideally- atomically sharp) metallic tip, whose movement may beprecisely controlled, is brought within a few Å(1Å =10-10m) of the studied surface and a bias voltage isapplied between them, so that the quantum-mechanical phe-nomenon of tunneling starts to take place. The extremesensitivity of the tunneling current (which typically decaysexponentially with increasing tip-surface distance) allows toobtain the topological image of the surface with atomicresolution, for example, by scanning the surface and recordingthe variations in the tunneling cur rent. The possibility tostudy superconductors in the superconducting state with STM isparticularly appealing, due to the ability of the STM todirectly measure the local density of states on the surface asthe derivative of the current-voltage characteristic. Thetechnique can be further enhanced by using a superconductingtip. In that case, the Josephson effect (coherent pairtunneling) may be achieved between the tip and the surface,which has been already demonstrated experimen tally. Thedependence of the critical Josephson current (the maximumsupercurrent which can be supported by the tip-surface"junction") on the superconducting properties of the surfaceallows to extract important information, such as the magnitudeand symmetry of the superconducting order parameter forhigh-temperature superconductors. A theoretical description ofsuch a junction was developed and studied for various setups,using the tunneling Hamiltonian formalism. Another possibleenhancement is based on the presence of spin-polarized intragapstates in the vicinity of a magnetic impurity, embedded in asuperconductor. In a conventional superconductor the couplingof these states to the environment is efficiently suppressed,leading to an assumption of a long decoherence time of theimpurityinduced states. An STM experiment to measure thisdecoherence time is proposed. If the measured decoherence timewill turn out to be large enough, new possibilities for precisespin-sensitive STM experiments with applications in spintronicsand quantum information processing will open.The final third part describes some efficient quantum MonteCarlo (QMC) techniques and their applications to stronglycorrelated models of bosons on a lattice. It covers two popularrepresentations of the partition function used in the QMC (thepath-integral representation and the stochastic seriesexpansion) and two efficient nonlocal updating schemes (loopand directed loop updates). Based on the coarse-grainedalgorithm for spin models with large total spin quantum numberS, an efficient algorithm for models of softcore bosons on thelattice is developed. Another application features the loopalgorithm, applied to a two-dimensional model, known as the t-Jzmodel, relevant to high-temperaturesuperconductivity, in the path-integral representation. A longstanding problem in the physics of high- temperaturesuperconductors is the origin of the inhomogeneous (stripe)phases, usually attributed to the long-range interactionsbetween the charge carriers. It is demonstrated, that thetwo-dimensional bosonic version of the anisotropic t-Jzmodel (a system of coupled one-dimensional chains)displays the stripe order for small values of inter-chaincoupling in the absence of any long-range interactions.Key words:mean field theory, magnetic multilayers,Curie temperature, compensationtemperature, scanning tunnelingmicroscopy, tunneling, superconductivity, high-temperaturesuperconductivity, local density of states, Josephson effect,tunneling Hamiltonian formalism, impurities in superconductors,T-matrix approximation, impurity-induced states, spinpolarization, decoherence time, quantum Monte Carlo,path-integral representation, stochastic series expansion, loopalgorithm, directed loops, softcore bosons, t-Jzmodel, inhomogeneous phases, stripes, topologicalorder, magnetic structure factor.