Higher dimensional Calabi-Yau manifolds of Kummer type

Based on Cynk-Hulek method we construct complex Calabi-Yau varieties of arbitrary dimensions using elliptic curves with automorphism of order 6. Also we give formulas for Hodge numbers of varieties obtained from that construction. We shall generalize result of Katsura and Sch\"utt to obtain arbitrarily dimensional Calabi-Yau manifolds which are Zariski in any characteristic $p\not\equiv 1\pmod{12}.$Comment: 13 pages, 2 figure

Strong Shift Equivalence of C∗C^*-correspondences

We define a notion of strong shift equivalence for $C^*$-correspondences and show that strong shift equivalent $C^*$-correspondences have strongly Morita equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong shift equivalent square matrices with non-negative integer entries give stably isomorphic Cuntz-Krieger algebras.Comment: 26 pages. Final version to appear in Israel Journal of Mathematic

Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands

We introduce and study two classes of Hubbard models with magnetic flux or with spin-orbit coupling, which have a flat lowest band separated from other bands by a nonzero gap. We study the Chern number of the flat bands, and find that it is zero for the first class but can be nontrivial in the second. We also prove that the introduction of on-site Coulomb repulsion leads to ferromagnetism in both the classes.Comment: 6 pages, 5 figure

Theory of magnetoelectric resonance in two-dimensional S=3/2S=3/2 antiferromagnet Ba2CoGe2O7{\rm Ba_2CoGe_2O_7} via spin-dependent metal-ligand hybridization mechanism

We investigate magnetic excitations in an $S=3/2$ Heisenberg model representing two-dimensional antiferromagnet ${\rm Ba_2CoGe_2O_7}$. In terahertz absorption experiment of the compound, Goldstone mode as well as novel magnetic excitations, conventional magnetic resonance at 2 meV and both electric- and magnetic-active excitation at 4 meV, have been observed. By introducing a hard uniaxial anisotropy term $\Lambda (S^z)^2$, three modes can be explained naturally. We also indicate that, via the spin-dependent metal-ligand hybridization mechanism, the 4 meV excitation is an electric-active mode through the coupling between spin and electric-dipole. Moreover, at 4 meV excitation, an interference between magnetic and electric responses emerges as a cross correlated effect. Such cross correlation effects explain the non-reciprocal linear directional dichroism observed in ${\rm Ba_2CoGe_2O_7}$.Comment: 5 pages, 3 figure

Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz

We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin-1/2 Heisenberg chains using the algebraic Bethe ansatz. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices which act on ${\bar {\mathscr H}}$, the tensor product of auxiliary spaces. By changing the basis in ${\bar {\mathscr H}}$, we derive explicit finite-dimensional representations for the matrices. These matrices are the same as those appearing in the recently proposed matrix product ansatz by Alcaraz and Lazo [Alcaraz F C and Lazo M J 2006 {\it J. Phys. A: Math. Gen.} \textbf{39} 11335.] apart from normalization factors. We also discuss the close relation between the matrix product representation of the Bethe eigenstates and the six-vertex model with domain wall boundary conditions [Korepin V E 1982 {\it Commun. Math. Phys.}, \textbf{86} 391.] and show that the change of basis corresponds to a mapping from the six-vertex model to the five-vertex model.Comment: 24 pages; minor typos are correcte

Spin 3/2 dimer model

We present a parent Hamiltonian for weakly dimerized valence bond solid states for arbitrary half-integral S. While the model reduces for S=1/2 to the Majumdar-Ghosh Hamiltonian we discuss this model and its properties for S=3/2. Its degenerate ground state is the most popular toy model state for discussing dimerization in spin 3/2 chains. In particular, it describes the impurity induced dimer phase in Cr8Ni as proposed recently. We point out that the explicit construction of the Hamiltonian and its main features apply to arbitrary half-integral spin S.Comment: 5+ pages, 6 figures; to appear in Europhysics Letter

Novel spin-liquid states in the frustrated Heisenberg antiferromagnet on the honeycomb lattice

Recent experiment on a honeycomb-lattice Heisenberg antiferromagnet (AF) Bi$_3$Mn$_4$O$_{12}$(NO$_3$) revealed a novel spin-liquid-like behavior down to low temperature, which was ascribed to the frustration effect due to the competition between the AF nearest- and next-nearest-neighbor interactions $J_1$ and $J_2$. Motivated by the experiment, we study the ordering of the $J_1$ -$J_2$ frustrated classical Heisenberg AF on a honeycomb lattice both by a low-temperature expansion and a Monte Carlo simulation. The model has been known to possess a massive degeneracy of the ground state, which, however, might be lifted due to thermal fluctuations leading to a unique ordered state, the effect known as 'order-by-disorder'. We find that the model exhibits an intriguing ordering behavior, particularly near the AF phase boundary. The energy scale of the order-by-disorder is suppressed there down to extremely low temperatures, giving rise to exotic spin-liquid states like a "ring-liquid" or a "pancake-liquid" state accompanied by the characteristic spin structure factor and the field-induced antiferromagnetism. We argue that the recent experimental data are explicable if the system is in such exotic spin-liquid states

Upravljanje silom mišićno-koštanog manipulatora pogonjenog spiralnim motorom

This paper presents force control of musculoskeletal manipulator driven by spiral motors. The kinematic and dynamic properties are shown to address the presence of ennvironmental contact with the manipulator. From this contact, the force control schemes were explored, by comparing between monoarticular-only structure and biarticular structure manipulator. Force control schemes were divided into independent muscle control, end effector step force command, and muscular viscoelasticity control. The results show advantages of biarticular actuation compared to monoarticular-only actuation in the feasibility of magnetic levitation (gap) control alongside force control.U ovome radu predstavljeno je upravljanje silom mišićno-koštanog manipulatora pogonjenog spiralnim motorom. Kinematička i dinamička svojstva prikazuju prisutnost kontakta manipulatora s okolinom. Na temelju kontakta istraženo je upravljanje silom usporedbom jednozglobne i dvozglobne strukture manipulatora. Upravljanje silom podijeljeno je u neovisno upravljanje mišićima, upravljanje alatom manipulatora (eng. end effector) i upravljanje mišićnom viskoelastičnosti. Rezultati pokazuju prednost dvozglobne strukture u odnosu na jednozglobnu u smislu izvedivosti upravljanja magnetskom levitacijom pored upravljanja silom

Cartan subalgebras and the UCT problem, II

We show that outer approximately represenbtable actions of a finite cyclic group on UCT Kirchberg algebras satisfy a certain quasi-freeness type property if the corresponding crossed products satisfy the UCT and absorb a suitable UHF algebra tensorially. More concretely, we prove that for such an action there exists an inverse semigroup of homogeneous partial isometries that generates the ambient C*-algebra and whose idempotent semilattice generates a Cartan subalgebra. We prove a similar result for actions of finite cyclic groups with the Rokhlin property on UCT Kirchberg algebras absorbing a suitable UHF algebra. These results rely on a new construction of Cartan subalgebras in certain inductive limits of Cartan pairs. We also provide a characterisation of the UCT problem in terms of finite order automorphisms, Cartan subalgebras and inverse semigroups of partial isometries of the Cuntz algebra $\mathcal{O}_2$. This generalizes earlier work of the authors.Comment: minor revisions; final version, accepted for publication in Math. Ann.; 26 page