Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions.

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

"Click Chip" Conjugation of Bifunctional Chelators to Biomolecules.

There is a growing demand for diagnostic procedures including in vivo tumor imaging. Radiometal-based imaging agents are advantageous for tumor imaging because radiometals (i) have a wide range of half-lives and (ii) are easily incorporated into imaging probes via a mild, rapid chelation event with a bifunctional chelator (BFC). Microfluidic platforms hold promise for synthesis of radiotracers because they can easily handle minute volumes, reduce consumption of expensive reagents, and minimize personnel exposure to radioactive compounds. Here we demonstrate the use of a "click chip" with an immobilized Cu(I) catalyst to facilitate the "click chemistry" conjugation of BFCs to biomolecules (BMs); a key step in the synthesis of radiometal-based imaging probes. The "click chip" was used to synthesize three different BM-BFC conjugates with minimal amounts of copper present in reaction solutions (∼20 ppm), which reduces or obviates the need for a copper removal step. These initial results are promising for future endeavors of synthesizing radiometal-based imaging agents completely on chip.

Development of a microfluidic "click chip" incorporating an immobilized Cu(I) catalyst.

We have developed a microfluidic "click chip" incorporating an immobilized Cu(I) catalyst for click reactions. The microfluidic device was fabricated from polydimethylsiloxane (PDMS) bonded to glass and featured ~14,400 posts on the surface to improve catalyst immobilization. This design increased the immobilization efficiency and reduces the reagents' diffusion time to active catalyst site. The device also incorporates five reservoirs to increase the reaction volume with minimal hydrodynamic pressure drop across the device. A novel water-soluble tris-(benzyltriazolylmethyl)amine (TBTA) derivative capable of stabilizing Cu(I), ligand 2, was synthesized and successfully immobilized on the chip surface. The catalyst immobilized chip surface was characterized by X-ray photoelectron spectroscopy (XPS). The immobilization efficiency was evaluated via radiotracer methods: the immobilized Cu(I) was measured as 1136±272 nmol and the surface immobilized Cu(I) density was 81±20 nmol cm-2. The active Cu(I)-ligand 2 could be regenerated up to five times without losing any catalyst efficiency. The "click" reaction of Flu568-azide and propargylamine was studied on chip for proof-of-principle. The on-chip reaction yields were ca. 82% with a 50 min reaction time or ca. 55% with a 15 min period at 37 °C, which was higher than those obtained in the conventional reaction. The on-chip "click" reaction involving a biomolecule, cyclo(RGDfK) peptide was also studied and demonstrated a conversion yield of ca. 98%. These encouraging results show promise on the application of the Cu(I) catalyst immobilized "click chip" for the development of biomolecule based imaging agents.