Quantum Monte Carlo studies of spinons in one-dimensional spin systems

Observing constituent particles with fractional quantum numbers in confined and deconfined states is an interesting and challenging problem in quantum many-body physics. Here we further explore a computational scheme [Y. Tang and A. W. Sandvik, Phys. Rev. Lett. {\bf 107}, 157201 (2011)] based on valence-bond quantum Monte Carlo simulations of quantum spin systems. Using several different one-dimensional models, we characterize $S=1/2$ spinon excitations using the spinon size and confinement length (the size of a bound state). The spinons have finite size in valence-bond-solid states, infinite size in the critical region, and become ill-defined in the N\'eel state. We also verify that pairs of spinons are deconfined in these uniform spin chains but become confined upon introducing a pattern of alternating coupling strengths (dimerization) or coupling two chains (forming a ladder). In the dimerized system an individual spinon can be small when the confinement length is large---this is the case when the imposed dimerization is weak but the ground state of the corresponding uniform chain is a spontaneously formed valence-bond-solid (where the spinons are deconfined). Based on our numerical results, we argue that the situation $\lambda \ll \Lambda$ is associated with weak repulsive short-range spinon-spinon interactions. In principle both the length-scales can be individually tuned from small to infinite (with $\lambda \le \Lambda$) by varying model parameters. In the ladder system the two lengths are always similar, and this is the case also in the dimerized systems when the corresponding uniform chain is in the critical phase. In these systems the effective spinon-spinon interactions are purely attractive and there is only a single large length scale close to criticality, which is reflected in the standard spin correlations as well as in the spinon characteristics.Comment: 15 pages, 15 figure

An investigation into reducing the spindle acceleration energy consumption of machine tools

Machine tools are widely used in the manufacturing industry, and consume large amount of energy. Spindle acceleration appears frequently while machine tools are working. It produces power peak which is highly energy intensive. As a result, a considerable amount of energy is consumed by this acceleration during the use phase of machine tools. However, there is still a lack of understanding of the energy consumption of spindle acceleration. Therefore, this research aims to model the spindle acceleration energy consumption of computer numerical control (CNC) lathes, and to investigate potential approaches to reduce this part of consumption. The proposed model is based on the principle of spindle motor control and includes the calculation of moment of inertia for spindle drive system. Experiments are carried out based on a CNC lathe to validate the proposed model. The approaches for reducing the spindle acceleration energy consumption were developed. On the machine level, the approaches include avoiding unnecessary stopping and restarting of the spindle, shortening the acceleration time, lightweight design, proper use and maintenance of the spindle. On the system level, a machine tool selection criterion is developed for energy saving. Results show that the energy can be reduced by 10.6% to more than 50% using these approaches, most of which are practical and easy to implement