F. Mila

Analysis of magnetic resonance experiments in YBa2Cu3O7

Abstract A consistent explanation of the unusual combination of anisotropies of the Knight shifts and relaxation rates of Cu(1) and Cu(2) nuclei in YBa2Cu3O7 is given. The key features are an anisotropic on-site hyperfine coupling to local Cu2+ electronic spins and an isotropic transferred hyperfine coupling to the neighboring Cu2+-spins. We use a quantum chemical model of the Cu-O hybridization to estimate the strength of these hyperfine interactions. Good agreement is found between our estimated parameters and experiment.

Ladders in a magnetic field: a strong coupling approach

Abstract:We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase (Hc1, Hc2, the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration.

LOW-ENERGY SECTOR OF THE S = 1/2 KAGOME ANTIFERROMAGNET

Starting from a modified version of the the S=1/2 Kagome antiferromagnet to emphasize the role of elementary triangles, an effective Hamiltonian involving spin and chirality variables is derived. A mean-field decoupling that retains the quantum nature of these variables is shown to yield a Hamiltonian that can be solved exactly, leading to the following predictions: i) The number of low lying singlet states increase with the number of sites N like 1.15 to the power N; ii) A singlet-triplet gap remains in the thermodynamic limit; iii) Spinons form boundstates with a small binding energy. By comparing these properties with those of the regular Kagome lattice as revealed by numerical experiments, we argue that this description captures the essential low energy physics of that model.

Quadrupolar phases of the S=1 bilinear-biquadratic heisenberg model on the triangular lattice

Using mean-field theory, exact diagonalizations, and SU(3) flavor theory, we have precisely mapped out the phase diagram of the S = 1 bilinear-biquadratic Heisenberg model on the triangular lattice in a magnetic field, with emphasis on the quadrupolar phases and their excitations. In particular, we show that ferroquadrupolar order can coexist with short-range helical magnetic order, and that the antiferroquadrupolar phase is characterized by a remarkable 2/3 magnetization plateau, in which one site per triangle retains quadrupolar order while the other two are polarized along the field. Implications for actual S=1 magnets are discussed.

Phase Diagram of the One-Dimensional Extended Hubbard Model at Quarter-Filling

We used exact diagonalization of small clusters and exact results in various limits to determine the phase diagram and the critical exponents of the one-dimensional (1D) U-V model at quarter-filling. We found an instability of the Luttinger liquid to a charge density wave (CDW) insulator across a boundary going from (U, V) = (+ ∞, 2t) to (4t, + ∞). In the metallic phase, the dominant fluctuations are superconducting if V is large enough and spin density wave (SDW) otherwise. In the latter case, the critical exponent α of the momentum distribution does not exceed 9/16. The relevance of these results to 1D organic conductors is discussed.

Magnetization plateaux and jumps in a class of frustrated ladders: A simple route to a complex behaviour

Abstract:We study the occurrence of plateaux and jumps in the magnetization curves of a class of frustrated ladders for which the Hamiltonian can be written in terms of the total spin of a rung. We argue on the basis of exact diagonalization of finite clusters that the ground state energy as a function of magnetization can be obtained as the minimum - with Maxwell constructions if necessary - of the energies of a small set of spin chains with mixed spins. This allows us to predict with very elementary methods the existence of plateaux and jumps in the magnetization curves in a large parameter range, and to provide very accurate estimates of these magnetization curves from exact or DMRG results for the relevant spin chains.

Charge gap in the one-dimensional dimerized Hubbard model at quarter-filling

We propose a quantitative estimate of the charge gap that opens in the one-dimensional dimerized Hubbard model at quarter-filling due to dimerization, which makes the system effectively half-filled, and to repulsion, which induces umklapp scattering processes. Our estimate is expected to be valid for any value of the repulsion and of the parameter describing the dimerization. It is based on analytical results obtained in various limits (weak coupling, strong coupling, large dimerization) and on numerical results obtained by exact diagonalization of small clusters. We consider two models of dimerization: alternating hopping integrals and alternating on-site energies. The former should be appropriate for the Bechgaard salts, the latter for compounds where the stacks are made of alternating TMTSF and TMTTF molecules.

Deducing correlation parameters from optical conductivity in the Bechgaard salts

Numerical calculations of the kinetic energy of various extensions of the one-dimensional Hubbard model including dimerization and repulsion between nearest neighbors are reported. Using the sum rule that relates the kinetic energy to the integral of the optical conductivity, one can detemine which parameters are consistent with the reduction of the infrared oscillator strength that has been observed in the Bechgaard salts. This leads to improved estimates of the correlation parameters for both the tetramethyltetraselenafulvalene and tetramethyltetrathiafulvalene series.

BIQUADRATIC INTERACTIONS AND SPIN-PEIERLS TRANSITION IN THE SPIN-1 CHAIN LIVGE2O6

The magnetic susceptibility of a new one-dimensional S=1 system, the vanadium oxide LiVGe2O6, has been measured. Contrary to previous S=1 chains, it exhibits an abrupt drop at 22 K typical of a spin-Peierls transition, and it is consistent with a gapless spectrum above this temperature. We propose that this behavior is due to the presence of a significant biquadratic exchange interaction, a suggestion supported by quantum chemistry calculations that take into account the quasidegeneracy of the t2g levels.

First-order transition between magnetic order and valence bond order in a 2D frustrated Heisenberg model

We study the competition between magnetic order and valence bond order in a two-dimensional (2D) frustrated Heisenberg model introduced some time ago by Shastry and Sutherland (Physica B, 108 (1981) 1069) for which a configuration of dimers is known to be the ground state in a certain range of parameters. Using exact diagonalization of small clusters, linear spin wave theory and Schwinger boson mean-field theory, we argue that the transition between the two types of order is first order, and that it takes place inside the domain where magnetic long-range order is stable with respect to quantum fluctuations.