Parity-broken ground state for the spin-1 pyrochlore antiferromagnet

The ground-state properties of the spin-1 pyrochlore antiferromagnet are studied by applying the VBS-like tetrahedron-unit decomposition to the original spin system. The symmetrization required on every vertex is taken into account by introducing a ferromagnetic coupling. The pairwise effective Hamiltonian between the adjacent tetrahedrons is obtained by considering the next nearest neighbor and the third neighbor exchange interactions. We find that the transverse component of the spin chirality exhibits a long-range order, breaking the parity symmetry of the tetrahedral group, while the chirality itself is not broken.Comment: 4 pages, 3 figures, REVTeX(ver.3.1

ICME international survey on teachers working and learning through collaboration

This article presents preliminary results from a survey commissioned for ICME 13 (2016) focusing on "Teachers Working and Learning Through Collaboration". It takes as a starting point a previous survey, commissioned for ICME 10 in 2004 that focused on Mathematics Teacher Education. The current survey focuses centrally on teachers involved in collaborations, sometimes in formal settings of professional development, but also in a more diverse range of collaborative settings including research initiatives. The roles of teachers involved in the collaboration, survey methods, decisions and limitations are described. While some of the findings to date resonate with those of the earlier survey, other findings highlight characteristics and issues relating to the differing ways in which teachers collaborate, either with other teachers or the various 'others', most notably mathematics teacher educator researchers. The roles and relationships that contribute to learning in such collaborations, as well as theories and methodologies found in survey sources, are a focus of the findings presented here. Studies rarely theorised collaboration, and few of those that did so reported explicitly on how their theoretical frame shaped the design of research methodologies/approaches guiding activities with teachers. One significant outcome has been the difficulty of relating teachers' learning to collaboration within a project, although many initiatives report developments in teaching, teacher learning and students' learning

Geometrical frustration induced (semi-)metal to insulator transition

We study the low-energy properties of the geometrically frustrated Hubbard model on a three-dimensional pyrochlore lattice and a two-dimensional checkerboard lattice on the basis of the renormalization group method and mean field analysis. It is found that in the half-filling case, a (semi-)metal to insulator transition (MIT) occurs. Also, in the insulating phase, which has a spin gap, the spin rotational symmetry is not broken, while charge ordering exists. The results are applied to the description of the MIT observed in the pyrochlore system ${\rm Tl_2Ru_2O_7}$.Comment: 4 pages, 5 figure

Classical generalized constant coupling model for geometrically frustrated antiferromagnets

A generalized constant coupling approximation for classical geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the magnetic susceptibility and specific heat are compared with Monte Carlo data for the classical Heisenberg model for the pyrochlore and kagome lattices. The predictions for the susceptibility are found to be essentially exact, and the corresponding predictions for the specific heat are found to be in very good agreement with the Monte Carlo results.Comment: 4 pages, 3 figures, 2 columns. Discussion about the zero T value of the pyrochlore specific heat correcte

Charge ordering in the spinels AlV2_2O4_4 and LiV2_2O4_4

We develop a microscopic theory for the charge ordering (CO) transitions in the spinels AlV$_2$O$_4$ and LiV$_2$O$_4$ (under pressure). The high degeneracy of CO states is lifted by a coupling to the rhombohedral lattice deformations which favors transition to a CO state with inequivalent V(1) and V(2) sites forming Kagom\'e and trigonal planes respectively. We construct an extended Hubbard type model including a deformation potential which is treated in unrestricted Hartree Fock approximation and describes correctly the observed first-order CO transition. We also discuss the influence of associated orbital order. Furthermore we suggest that due to different band fillings AlV$_2$O$_4$ should remain metallic while LiV$_2$O$_4$ under pressure should become a semiconductor when charge disproportionation sets in

Metal-insulator transition in the two-orbital Hubbard model at fractional band fillings: Self-energy functional approach

We investigate the infinite-dimensional two-orbital Hubbard model at arbitrary band fillings. By means of the self-energy functional approach, we discuss the stability of the metallic state in the systems with same and different bandwidths. It is found that the Mott insulating phases are realized at commensurate band fillings. Furthermore, it is clarified that the orbital selective Mott phase with one orbital localized and the other itinerant is stabilized even at fractional band fillings in the system with different bandwidths.Comment: 7 pages, 10 figure

Stability of a metallic state in the two-orbital Hubbard model

Electron correlations in the two-orbital Hubbard model at half-filling are investigated by combining dynamical mean field theory with the exact diagonalization method. We systematically study how the interplay of the intra- and inter-band Coulomb interactions, together with the Hund coupling, affects the metal-insulator transition. It is found that if the intra- and inter-band Coulomb interactions are nearly equal, the Fermi-liquid state is stabilized due to orbital fluctuations up to fairly large interactions, while the system is immediately driven to the Mott insulating phase away from this condition. The effects of the isotropic and anisotropic Hund coupling are also addressed.Comment: 7 pages, 9 figure

Critical Dynamics of Singlet Excitations in a Frustrated Spin System

We construct and analyze a two-dimensional frustrated quantum spin model with plaquette order, in which the low-energy dynamics is controlled by spin singlets. At a critical value of frustration the singlet spectrum becomes gapless, indicating a quantum transition to a phase with dimer order. This T=0 transition belongs to the 3D Ising universality class, while at finite temperature a 2D Ising critical line separates the plaquette and dimerized phases. The magnetic susceptibility has an activated form throughout the phase diagram, whereas the specific heat exhibits a rich structure and a power law dependence on temperature at the quantum critical point. We argue that the novel quantum critical behavior associated with singlet criticality discussed in this work can be relevant to a wide class of quantum spin systems, such as antiferromagnets on Kagome and pyrochlore lattices, where the low-energy excitations are known to be spin singlets, as well as to the CAVO lattice and several recently discovered strongly frustrated square-lattice antiferromagnets.Comment: 5 pages, 5 figures, additional discussion and figure added, to appear in Phys. Rev.