Frustrated three-leg spin tubes: from spin 1/2 with chirality to spin 3/2

Motivated by the recent discovery of the spin tube [(CuCl$_2$tachH)$_3$Cl]Cl$_2$, we investigate the properties of a frustrated three-leg spin tube with antiferromagnetic intra-ring and inter-ring couplings. We pay special attention to the evolution of the properties from weak to strong inter-ring coupling and show on the basis of extensive density matrix renormalization group and exact diagonalization calculations that the system undergoes a first-order phase transition between a dimerized gapped phase at weak coupling that can be described by the usual spin-chirality model and a gapless critical phase at strong coupling that can be described by an effective spin-3/2 model. We also show that there is a magnetization plateau at 1/3 in the gapped phase and slightly beyond. The implications for [(CuCl$_2$tachH)$_3$Cl]Cl$_2$ are discussed, with the conclusion that this system behaves essentially as a spin-3/2 chain.Comment: 8 pages, 9 figures, revised versio

Identification de QTL pour le rendement, les caractéristiques des fèves et la résistance à Phytophthora Palmivora chez Theobroma Cacao L.

Cette étude visait à cartographier les QTL qui contrôlent les caractéristiques de rendement des fèves et la résistance à Phytophthora palmivora dans trois descendances en ségrégation : une issue de croisements (SCA6 x. H) x Cl, deux descendances pleins-frères issus de (P7 x ICS100) et (PY x. ICS95) x Cl. Des plants âgés d'environ ID ans ont fait l'objet d'un suivi individuel pendant trois périodes de récolte par rapport à la pourriture brune des cabosses de Phytophthora (PPR), pour les caractéristiques liées au rendement et aux fèves. La résistance à Phytophthora des descendances pleins-frères a aussi été évaluée par essai sur disques de feuilles. Des cartes génétiques, basées uniquement sur les marqueurs SSR, ont été construites avec 127, 128 et 179 individus, respectivement. Quatorze et sept QTL pour les caractéristiques de rendement ont été détectés sur les parents (P7 x ICS100) et (P7 x ICS95) respectivement. Les chromosomes 4 et 10 sont les chromosomes ancres pour les QTL de rendement entre les parents. Vingt-sept et dix-huit QTL pour les caractéristiques des fèves ont été cartographiés chez les parents (P7 x ICS100) et (P7 x ICS95) respectivement. Le chromosome 4 portait le nombre le plus élevé de QTL de différentes caractéristiques de fèves. Globalement, les QTL de caractéristiques de rendement et de fèves sont colocalisés. Les QTL étaient plus stables au fil des ans, en particulier pendant la période de récolte principale. Pour le PPR., 3, 2 et 3 QTL ont été identifiés respectivement pour les parents (P7 x H), (P7 x ICS95) et (SCA6 x ICS95). Trois QTL de résistance foliaire ont été identifiés sur les chromosomes 1, 2 et 10 des parents (P7 x ICS100). Un QTL PPR chez le parent " SCA6 x H " et un QTL de résistance foliaire chez le parent " P7 x ICS100 >> ont été détectés sur le chromosome 1. Certains QTL d'une caractéristique (résistance, rendement, fèves) ont été trouvés sur plusieurs chromosomes d'un ou plusieurs parents. En regroupant les parents (SCA6 x H) et (P7 x ICS100), une région de QTL PPR a été identifiée sur le chromosome 6. Par ailleurs, certains des QTL des caractéristiques étudiées étaient situés dans les mêmes régions chromosomiques que ceux qui avaient été identifiés dans les études précédentes. Certains autres ont été détectés pour la première fois dans l'étude actuelle. Certains QTL ont été détectés dans les deux familles, alors que d'autres étaient uniquement présents dans une famille. Nos résultats montrent que la sélection de génotypes pour la production cacaoyère peut se faire sur la base des informations sur les fèves. Les marqueurs associés aux QTL identifiés sur des chromosomes particuliers, le chromosome 4 par exemple, sont les meilleurs candidats pour le développement d'outils de sélection. Par conséquent, une plus grande attention doit être accordée à ces chromosomes pour des études plus approfondies, associant des génotypes de différents matériels génétiques. (Texte intégral

Quantum Heisenberg antiferromagnet on low-dimensional frustrated lattices

Using a lattice-gas description of the low-energy degrees of freedom of the quantum Heisenberg antiferromagnet on the frustrated two-leg ladder and bilayer lattices we examine the magnetization process at low temperatures for these spin models. In both cases the emergent discrete degrees of freedom implicate a close relation of the frustrated quantum Heisenberg antiferromagnet to the classical lattice gas with finite nearest-neighbor repulsion or, equivalently, to the Ising antiferromagnet in a uniform magnetic field. Using this relation we obtain analytical results for thermodynamically large systems in the one-dimensional case. In the two-dimensional case we perform classical Monte Carlo simulations for systems of up to $100 \times 100$ sites.Comment: Submitted to Teoreticheskaya i Matematicheskaya Fizika (special issue dedicated to the 90th anniversary of Professor Sergei Vladimirovich Tyablikov

On the valence-bond solid phase of the crossed-chain quantum spin model

Using a series expansion based on the flow-equation method we study the ground state energy and the elementary triplet excitations of a generalized model of crossed spin-1/2 chains starting from the limit of decoupled quadrumers. The triplet dispersion is shown to be very sensitive to the inter-quadrumer frustration, exhibiting a line of almost complete localization as well as lines of quantum phase transitions limiting the stability of the valence-bond solid phase. In the vicinity of the checkerboard-point a finite window of exchange couplings is found with a non-zero spin-gap, consistent with known results from exact diagonalization. The ground state energy is lower than that of the bare quadrumer case for all exchange couplings investigated. In the limiting situation of the fully frustrated checkerboard magnet our results agree with earlier series expansion studies.Comment: 8 pages, 7 figure

Spin-1/2 frustrated antiferromagnet on a spatially anisotopic square lattice: contribution of exact diagonalizations

The phase diagram of a spin-1/2 $J-J'-J_2$ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the $J_1-J_2$ model on the square lattice with two different nearest-neighbor couplings $J,J'$ and may be also viewed as an array of coupled Heisenberg chains. The results suggest that the resonnating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B {\bf 67}, 024422 (2003)] for $J_2=0.5J' \ll J$ is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum. This line is likely bordered on both side by a columnar dimer long range order. This columnar order could extends for $J'\to J$ which correspond to the $J_1-J_2$ model.Comment: 14 pages, 21 figures, final versio

Motion of Bound Domain Walls in a Spin Ladder

The elementary excitation spectrum of the spin-$\frac{1}{2}$ antiferromagnetic (AFM) Heisenberg chain is described in terms of a pair of freely propagating spinons. In the case of the Ising-like Heisenberg Hamiltonian spinons can be interpreted as domain walls (DWs) separating degenerate ground states. In dimension $d>1$, the issue of spinons as elementary excitations is still unsettled. In this paper, we study two spin-$\frac{1}{2}$ AFM ladder models in which the individual chains are described by the Ising-like Heisenberg Hamiltonian. The rung exchange interactions are assumed to be pure Ising-type in one case and Ising-like Heisenberg in the other. Using the low-energy effective Hamiltonian approach in a perturbative formulation, we show that the spinons are coupled in bound pairs. In the first model, the bound pairs are delocalized due to a four-spin ring exchange term in the effective Hamiltonian. The appropriate dynamic structure factor is calculated and the associated lineshape is found to be almost symmetric in contrast to the 1d case. In the case of the second model, the bound pair of spinons lowers its kinetic energy by propagating between chains. The results obtained are consistent with recent theoretical studies and experimental observations on ladder-like materials.Comment: 12 pages, 7 figure

Bond order from disorder in the planar pyrochlore magnet

We study magnetic order in the Heisenberg antiferromagnet on the checkerboard lattice, a two-dimensional version of the pyrochlore network with strong geometric frustration. By employing the semiclassical (1/S) expansion we find that quantum fluctuations of spins induce a long-range order that breaks the four-fold rotational symmetry of the lattice. The ordered phase is a valence-bond crystal. We discuss similarities and differences with the extreme quantum case S = 1/2 and find a useful phenomenology to describe the bond-ordered phases.Comment: Minor clarifications + reference to an informal introduction cond-mat/030809

Quantum phases and phase transitions of Mott insulators

This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. The simplest class of Mott insulators have an even number of S=1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic field. The case of an odd number of S=1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S=1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories (T. Senthil et al., cond-mat/0312617) of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-Ginzburg-Wilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations.Comment: 51 pages, 13 figure

Strong-coupling expansion and effective hamiltonians

When looking for analytical approaches to treat frustrated quantum magnets, it is often very useful to start from a limit where the ground state is highly degenerate. This chapter discusses several ways of deriving {effective Hamiltonians} around such limits, starting from standard {degenerate perturbation theory} and proceeding to modern approaches more appropriate for the derivation of high-order effective Hamiltonians, such as the perturbative continuous unitary transformations or contractor renormalization. In the course of this exposition, a number of examples taken from the recent literature are discussed, including frustrated ladders and other dimer-based Heisenberg models in a field, as well as the mapping between frustrated Ising models in a transverse field and quantum dimer models.Comment: To appear as a chapter in "Highly Frustrated Magnetism", Eds. C. Lacroix, P. Mendels, F. Mil