Robust Hund rule without Coulomb repulsion and exclusion principle in quantum antiferromagnetic chains of composite half spins.

Quantum spin chains with composite spins have been used to approximate conventional chains with higher spins. For instance, a spin 1 (or [Formula: see text]) chain was sometimes approximated by a chain with two (or three) spin [Formula: see text]'s per site. However, little examination has been given as to whether this approximation, effectively assuming the first Hund rule per site, is valid and why. In this paper, the validity of this approximation is investigated numerically. We diagonalize the Hamiltonians of spin chains with a spin 1 and [Formula: see text] per site and with two and three spin [Formula: see text]'s per site. The low energy excitation spectrum for the spin chain with M spin [Formula: see text]'s per site is found to coincide with that of the corresponding conventional chain with one spin [Formula: see text] per site. In particular, we find that as the system size increases, an increasingly larger block of consecutive lowest energy states with maximal spin per site is observed, robustly supporting the first Hund rule even though the exclusion principle does not apply and the system does not possess Coulomb repulsion. As for why this approximation works, we show that this effective Hund rule emerges as a plausible consequence when applying to composite spin systems the Lieb-Mattis theorem, which is originally for the ground state of ferrimagnetic and antiferromagnetic spin systems.

Improving series convergence: the simple pendulum and beyond.

A simple and easy to implement method for improving the convergence of a power series is presented. We observe that the most obvious or analytically convenient point about which to make a series expansion is not always the most computationally efficient. Series convergence can be dramatically improved by choosing the center of the series expansion to be at or near the average value at which the series is to be evaluated. For illustration, we apply this method to the well-known simple pendulum and to the Mexican hat type of potential. Large performance gains are demonstrated. While the method is not always the most computationally efficient on its own, it is effective, straightforward, quite general, and can be used in combination with other methods.

Modeling the nanoscratching of self-healing materials.

We use computational modeling to determine the mechanical response of crosslinked nanogels to an atomic force microscope (AFM) tip that is moved through the sample. We focus on two-dimensional systems where the nanogels are interconnected by both strong and labile bonds. To simulate this system, we modify the lattice spring model (LSM) to extend the applicability of this method to a broader range of elastic materials. Via this modified LSM, we model each nanogel as a deformable particle. We utilize the Bell model to describe the bonds between these nanogel particles, and subsequently, simulate the rupturing of bonds due to the force exerted by the moving indenter. The ruptured labile bonds can readily reform and thus can effectively mend the cavities formed by the moving AFM tip. We determine how the fraction of labile bonds, the nanogel stiffness, and the size and velocity of the moving tip affect the self-healing behavior of the material. We find that samples containing just 10% of labile bonds can heal to approximately 90% of their original, undeformed morphology. Our results provide guidelines for creating reconfigurable materials that can undergo self-repair and thereby withstand greater mechanical stress under everyday use.