Hamiltonian triangular refinements and space-filling curves

We have introduced here the concept of Hamiltonian triangular refinement. For any Hamiltonian triangulation it is shown that there is a refinement which is also a Hamiltonian triangulation and the corresponding Hamiltonian path preserves the nesting condition of the corresponding space-filling curve. We have proved that the number of such Hamiltonian triangular refinements is bounded from below and from above. The relation between Hamiltonian triangular refinements and space-filling curves is also explored and explained

Novel Graph-based Adaptive Triangular Mesh Refinement for Finite-volume Discretizations

A novel graph-based adaptive mesh refinement technique for triangular finite-volume discretizations in order to solve second-order partial differential equations is described. Adaptive refined meshes are built in order to solve time-dependent problems aiming low computational costs. In the approach proposed, flexibility to link and traverse nodes among neighbors in different levels of refinement is admitted; and volumes are refined using an approach that allows straightforward and strictly local update of the data structure. In addition, linear equation system solvers based on the minimization of functionals can be easily used; specifically, the Conjugate Gradient Method. Numerical and analytical tests were carried out in order to study the required execution time and the data storage cost. These tests confirmed the advantages of the approach proposed in elliptic and parabolic problems

Finite temperature strong-coupling expansions for the Kondo lattice model

Strong-coupling expansions, to order $(t/J)^8$, are derived for the Kondo lattice model of strongly correlated electrons, in 1-, 2- and 3- dimensions at arbitrary temperature. Results are presented for the specific heat, and spin and charge susceptibilities.Comment: revtex

The Synthesis and Characterization of New Triangular Lattice Compounds with Exotic Magnetic Ground States

The foundation of experimental condensed matter physics is comprised of two material processes, synthesis and characterization. For most measurements, single crystal samples are preferred as they allow spatially dependent information to be obtained. On the other hand, polycrystalline samples are also critical as they reveal bulk properties of the material and are generally much easier to produce. Material characterization then relies on accurately measuring a material\u27s physical, electrical, and magnetic properties using a variety of different techniques.In this dissertation, we focus on triangular lattice antiferromagnets (TLAFs) which have been studied because of their great potential to exhibit various intriguing magnetic properties related to strong geometrical frustration. Recent studies of TLAFs mainly explore four central themes: quantum spin liquid (QSL) states, exotic disordered states, the coplanar 120 degree state and the related field induced spin state transitions, and multiferroicity. Accordingly, we have investigated two materials which fall into these categories. The first is the magnetodielectric material RCr(BO3)2 (R = Y and Ho), and the second is a group of Mo-cluster compounds including the quantum spin liquid candidate Li2In1-xScxMo3O8 and the ferromagnets (Mg,Zn)ScMo3O8. Both materials have been investigated using x-ray diffraction, powder neutron diffraction, ac and dc susceptibility, and specific heat capacity measurements as well as other complementary techniques. A discussion of these results as well as potential future experiments are included

Electronic structure and magnetic properties of the spin-1/2 Heisenberg system CuSe2O5

A microscopic magnetic model for the spin-1/2 Heisenberg chain compound CuSe2O5 is developed based on the results of a joint experimental and theoretical study. Magnetic susceptibility and specific heat data give evidence for quasi-1D magnetism with leading antiferromagnetic (AFM) couplings and an AFM ordering temperature of 17 K. For microscopic insight, full-potential DFT calculations within the local density approximation (LDA) were performed. Using the resulting band structure, a consistent set of transfer integrals for an effective one-band tight-binding model was obtained. Electronic correlations were treated on a mean-field level starting from LDA (LSDA+U method) and on a model level (Hubbard model). In excellent agreement of experiment and theory, we find that only two couplings in CuSe2O5 are relevant: the nearest-neighbour intra-chain interaction of 165 K and a non-frustrated inter-chain coupling of 20 K. From a comparison with structurally related systems (Sr2Cu(PO4)2, Bi2CuO4), general implications for a magnetic ordering in presence of inter-chain frustration are made.Comment: 20 pages, 8 figures, 3 table

Electronic correlation in the quantum Hall regime

Two-dimensional interacting electron systems become strongly correlated if the electrons are subject to a perpendicular high magnetic field. After introducing the physics of the quantum Hall regime the incompressible many- particle ground state and its excitations are studied in detail at fractional filling factors for spin-polarized electrons. The spin degree of freedom whose importance was shown in recent experiments is considered by studying the thermodynamics at filling factor one and near one.Comment: 55 pages, 26 eps-figure

Sign-alternating interaction mediated by strongly correlated lattice bosons

We reveal a generic mechanism of generating sign-alternating intersite interactions mediated by strongly correlated lattice bosons. The ground-state phase diagram of the two-component hard-core Bose–Hubbard model on a square lattice at half-integer filling factor for each component, obtained by worm algorithm Monte Carlo simulations, is strongly modified by these interactions and features the solid+superfluid (SF) phase for strong asymmetry between the hopping amplitudes. The new phase is a direct consequence of the effective nearest-neighbor repulsion between \u27heavy\u27 atoms mediated by the \u27light\u27 SF component. Due to their sign-alternating character, mediated interactions lead to a rich variety of yet to be discovered quantum phases