Exact diagonalization Studies of Two-dimensional Frustrated Antiferromagnet Models

We describe the four kinds of behavior found in two-dimensional isotropic quantum antiferromagnets. Two of them display long range order at T=0: the N\'eel state and the Valence Bond Crystal. The last two are Spin-Liquids. Properties of these different states are shortly described and open questions are underlined.Comment: 7 pages; invited talk at "HFM 2000" (Waterloo, June 2000); submitted to Can. J. Phy

An investigation of the quantum J1−J2−J3J_1-J_2-J_3 model on the honeycomb lattice

We have investigated the quantum $J_1-J_2-J_3$ model on the honeycomb lattice with exact diagonalizations and linear spin-wave calculations for selected values of $J_{2}/J_{1}$, $J_{3}/J_{1}$ and antiferromagnetic ($J_{1}>0$) or ferromagnetic ($J_{1}<0$) nearest neighbor interactions. We found a variety of quantum effects: "order by disorder" selection of a N{\'e}el ordered ground-state, good candidates for non-classical ground-states with dimer long range order or spin-liquid like. The purely antiferromagnetic Heisenberg model is confirmed to be N{\'e}el ordered. Comparing these results with those observed on the square and triangular lattices, we enumerate some conjectures on the nature of the quantum phases in the isotropic models.Comment: 14 pages, 22 Postscript figures, uses svjour.cls and svepj.clo, submitted to European Physical Journal B: condensed matter physi

Field-induced gap in ordered Heisenberg antiferromagnets

Heisenberg antiferromagnets in a strong uniform magnetic field $H$ are expected to exhibit a gapless phase with a global O(2) symmetry. In many real magnets, a small energy gap is induced by additional interactions that can be viewed as a staggered transverse magnetic field $h = c H$, where $c$ is a small proportionality constant. We study the effects of such a perturbation, particularly for magnets with long-range order, by using several complimentary approaches: numerical diagonalizations of a model with long-range interactions, classical equations of motion, and scaling arguments. In an ordered state at zero temperature, the energy gap at first grows as $(cH)^{1/2}$ and then may dip to a smaller value, of order $(cH)^{2/3}$, at the quantum critical point separating the ``gapless'' phase from the gapped state with saturated magnetization. In one spatial dimension, the latter exponent changes to 4/5.Comment: 6 pages, 5 figure

Quantum spin liquids: a large-S route

This paper explores the large-S route to quantum disorder in the Heisenberg antiferromagnet on the pyrochlore lattice and its homologues in lower dimensions. It is shown that zero-point fluctuations of spins shape up a valence-bond solid at low temperatures for one two-dimensional lattice and a liquid with very short-range valence-bond correlations for another. A one-dimensional model demonstrates potential significance of quantum interference effects (as in Haldane's gap): the quantum melting of a valence-bond order yields different valence-bond liquids for integer and half-integer values of S.Comment: Proceedings of Highly Frustrated Magnetism 2003 (Grenoble), 6 LaTeX page

Structural Transition of Li2RuO3 Induced by Molecular-Orbit Formation

A pseudo honeycomb system Li2RuO3 exhibits a second-order-like transition at temperature T=Tc=540 K to a low-T nonmagnetic phase with a significant lattice distortion forming Ru-Ru pairs. For this system, we have calculated the band structure, using the generalized gradient approximation (GGA) in both the high- and low- T phases, and found that the results of the calculation can naturally explain the insulating behavior observed in the low-T phase. The detailed characters of the Ru 4d t2g bands obtained by the tight-binding fit to the calculated dispersion curves show clear evidence that the structural transition is driven by the formation of the Ru-Ru molecular-orbits, as proposed in our previous experimental studies.Comment: 5 pages, 5 figures, 4 tables, submitted to J. Phys. Soc. Jp

Condensation of magnons and spinons in a frustrated ladder

Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a one-dimensional version of this problem, a frustrated ladder with a magnetization plateau at m=1/2. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaux. In particular, anisotropic interactions generically open a gap in the region between the plateaux, but we show that this gap closes upon entering fractional plateaux. All of these conclusions, based on analytical arguments, are supported by extensive Density Matrix Renormalization Group calculations.Comment: 15 pages, 15 figures. minor changes in tex

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

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