Introduction to the Bethe ansatz II

Building on the fundamentals introduced in part I, we employ the Bethe ansatz to study some ground-state properties (energy, magnetization, susceptibility) of the one-dimensional s=1/2 Heisenberg antiferromagnet in zero and nonzero magnetic field. The 2-spinon triplet and singlet excitations from the zero-field ground state are discussed in detail, and their energies are calculated for finite and infinite chains. Procedures for the numerical calculation of real and complex solutions of the Bethe ansatz equations are discussed and applied. The paper is designed as a tutorial for beginning graduate students. It includes 10 problems for further study.Comment: 9 pages, 5 figure

Dynamics of quantum spin systems in dimer and valence-bond solid ground states stabilized by competing interactions

For special coupling ratios, the one-dimensional (1D) s=1/2 Heisenberg model with antiferromagnetic nearest and next-nearest neighbor interactions has a pure dimer ground state, and the 1D s=1 Heisenberg model with antiferromagnetic bilinear and biquadratic interactions has an exact valence-bond-solid ground state. The recursion method is used to calculate the T=0 spin dynamic structure factor for both models and, for the s=1/2 model, also the dimer dynamic structure factor. New results for line shapes and dynamically relevant dispersions are obtained.Comment: RevTex file, 3 ps figure

Impact of Criticality and Phase Separation on the Spin Dynamics of the One-Dimensional t–J Model

The recursion method is used to determine the T=0 spin dynamic structure factor S zz (q,ω) in the Luttinger liquid state and in the phase‐separated state of the one‐dimensional t–J model. As the exchange coupling increases from zero, the dispersions and line shapes of the dominant spin excitations are observed to undergo a major metamorphosis between the free‐fermion limit and the onset of phase separation. The familiar two‐spinon spectrum of the Heisenberg antiferromagnetic chain emerges gradually in the strongly phase‐separated state

Order-Parameter Fluctuations in the Frustrated Heisenberg Model on the Square Lattice

The T=0 dynamics of the two‐dimensional s=1/2 Heisenberg model with competing nearest‐neighbor (J 1) and next‐nearest‐neighbor (J 2) interactions is explored via the recursion method, specifically the frequency‐dependent fluctuations of the order parameters associated with some of the known or suspected ordering tendencies in this system, i.e., Néel, collinear, dimer, and chiral order. The results for the dynamic structure factors of the respective fluctuation operators show a strong indication of collinear order at J 2/J 1≳0.6 and a potential for dimer order at 0.5≲J 2/J 1≲0.6, whereas the chiral ordering tendency is observed to be considerably weaker

Conceptional Design of Self-Assembling Bisubstrate-like Inhibitors of Protein Kinase A Resulting in a Boronic Acid Glutamate Linkage

The spontaneous esterification of boronic acids with polyols provides a promising opportunity to generate self-assembled bisubstrate-like inhibitors within the binding pocket of cAMP-dependent protein kinase (PKA). As a first substrate component, we designed amino acids, which have either a boronic acid or ribopyranose side chain and introduced them to the substrate-like peptide protein kinase inhibitor (PKI). The second component was derived from the active-site inhibitor Fasudil, which was functionalized with phenylboronic acid. NMR spectroscopy in dimethylsulfoxide proved spontaneous reversible condensation of both components. Reinforced by the protein environment, both separately bound substrates were expected to react via boronic-ester formation bridging the two binding sites of PKA. Multiple crystal structures of PKA with bound PKIs, positionally modified with residues such as a ribopyranosylated serine and threonine or a phenylboronic acid attached to lysine via amide bonds, were determined with the phenylboronic acid-linked Fasudil. Although PKA accepts both inhibitors simultaneously, the expected covalent attachment between both components was not observed. Instead, spontaneous reaction of the terminal boronic acid group of the modified Fasudil with the carboxylate of Glu127 was detected once the latter residue is set free from a strong salt bridge formed with arginine by the original peptide inhibitor PKI. Thus, the desired self-assembly reaction occurs spontaneously in the protein environment by an unexpected carboxylic acid boronate complex. To succeed with our planned self-assembly reaction between both substrate components, we have to redesign the required reaction partners more carefully to finally yield the desired bisubstrate-like inhibitors in the protein environment

Superparamagnetic Luminescent MOF@Fe₃O₄/SiO₂ Composite Particles for Signal Augmentation by Magnetic Harvesting as Potential Water Detectors

Herein, we present the generation of a novel complex particle system consisting of superparamagnetic Fe₃O₄/SiO₂ composite microparticle cores, coated with luminescent metal–organic frameworks (MOFs) of the constitution _∞²[Ln₂Cl₆(bipy)₃]·2bipy (bipy = 4,4′-bipyridine) that was achieved by intriguing reaction conditions including mechanochemistry. The novel composites combine the properties of both constituents: superparamagnetism and luminescence. The magnetic properties can be exploited to magnetically collect the particles from dispersions in fluids and, by gathering them at one spot, to augment the luminescence originating from the MOF modification on the particles. The luminescence can be influenced by chemical compounds, e.g., by quenching observed for low concentrations of water. Thus, the new composite systems present an innovative concept of property combination that can be potentially used for the detection of water traces in organic solvents as a magnetically augmentable, luminescent water detector

Homoleptic Lanthanide 1,2,3-Triazolates _∞^2–3[Ln(Tz*)₃] and Their Diversified Photoluminescence Properties

The series of homoleptic lanthanide 1,2,3-triazolates _∞³[Ln­(Tz*)₃] (Ln³⁺ = lanthanide cation, Tz*^– = 1,2,3-triazolate anion, C₂H₂N₃^–) is completed by synthesis of the three-dimensional (3D) frameworks with Ln = La, Ce, Pr, Nd, and Sm, and characterization by X-ray powder diffraction, differential thermal analysis-thermogravimetry (DTA/TG) investigations and molecular vibration analysis. In addition, α-_∞²[Sm­(Tz*)₃], a two-dimensional polymorph of 3D β-_∞³[Sm­(Tz*)₃], is presented including the single crystal structure. The 3D lanthanide triazolates form an isotypic series of the formula _∞³[Ln­(Tz*)₃] ranging from La to Lu, with the exception of Eu, which forms a mixed valent metal organic framework (MOF) of different structure and the constitution _∞³[Eu­(Tz*)_6+<i>x</i>(Tz*H)_2–<i>x</i>]. The main focus of this work is put on the investigation of the photoluminescence behavior of lanthanide 1,2,3-triazolates _∞³[Ln­(Tz*)₃] and illuminates that six different luminescence phenomena can be found for one series of isotypic compounds. The luminescence behavior of the majority of these compounds is based on the photoluminescence properties of the organic linker molecules. Differing properties are observed for _∞³[Yb­(Tz*)₃], which exhibits luminescence properties based on charge transfer transitions between the linker and Yb³⁺ ions, and for _∞³[Ce­(Tz*)₃] and _∞³[Tb­(Tz*)₃], in which the luminescence properties are a combination of the ligand and the lanthanide metal. In addition, strong inner-filter effects are found in the ligand emission bands that are attributed to reabsorption of the emitted light by the trivalent lanthanide ions. Antenna effects of varying efficiency are present indicated by the energy being transferred to the lanthanide ions subsequent to excitation of the ligand. _∞³[Ce­(Tz*)₃] shows a 5d-4f induced intense blue emission upon excitation with UV light, while _∞³[Tb­(Tz*)₃] shows emission in the green region of the visible spectrum, which can be identified with 4f-4f-transitions typical for Tb³⁺ ions