Measuring Majorana fermions qubit state and non-Abelian braiding statistics in quenched inhomogeneous spin ladders

We study the Majorana fermions (MFs) in a spin ladder model. We propose and numerically show that the MFs qubit state can be read out by measuring the fusion excitation in the quenched inhomogeneous spin ladders. Moreover, we construct an exactly solvable T-junction spin ladder model, which can be used to implement braiding operations of MFs. With the braiding processes simulated numerically as non-equilibrium quench processes, we verify that the MFs in our spin ladder model obey the non-Abelian braiding statistics. Our scheme not only provides a promising platform to study the exotic properties of MFs, but also has broad range of applications in topological quantum computation.Comment: 5+3 pages, 6 figure

Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets

By using the density matrix renormalization group, we study the spin-liquid phases of spin-$1/2$ XXZ kagome antiferromagnets. We find that the emergence of spin liquid phase does not depend on the anisotropy of the XXZ interaction. In particular, the two extreme limits---Ising (strong $S^z$ interaction) and XY (zero $S^z$ interaction)---host the same spin-liquid phases as the isotropic Heisenberg model. Both the time-reversal-invariant spin liquid and the chiral spin liquid with spontaneous time-reversal symmetry breaking are obtained. We show they evolve continuously into each other by tuning the second- and third-neighbor interactions. At last, we discuss the possible implication of our results on the nature of spin liquid in nearest neighbor XXZ kagome antiferromagnets, including the most studied nearest neighbor spin-$1/2$ kagome anti-ferromagnetic Heisenberg model

Multivariate Analysis of Variance for Simple Designs

The analysis of variance is a well known tool for testing how treatments change the average response of experimental units. The essence of the procedure is to compare the variation among means of groups of units subjected to the same treatment with the within treatment variation. If the variation among means is large with respect to the within group variation we are likely to conclude that the treatments caused the variation and hence we say the treatments cause some change in the group means. The usual analysis of variance checks how far apart the group means are in a single scale of measurement. Almost all researchers are interested in how the treatments affect more than one characteristic (variable) of their experimental units. A typical usage of such data is to run a standard analysis of variance on each variable. This procedure can be very misleading when trying to interpret the results. Most of the time there are strong correlations among these variables and hence if one variable tests significant the others will also. The multivariate analysis of variance provides a way of performing valid tests regardless of the correlation structure among the variables of interest