Spinon excitation spectra of the J1J_1-J2J_2 chain from analytical calculations in the dimer basis and exact diagonalization

The excitation spectrum of the frustrated spin-$1/2$ Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at $J_2=0.25J_1$ and an onset of incommensurability in the dispersion relation at $J_2=9/17J_1$ [as in S. Brehmer \emph{et al.}, J. Phys.: Condens. Matter \textbf{10}, 1103 (1998)]. These analytical results provide a good support for the understanding of exact diagonalization spectra, assuming an independent spinons picture.Comment: 11 pages, 6 figure

Magnetic responses of randomly depleted spin ladders

The magnetic responses of a spin-1/2 ladder doped with non-magnetic impurities are studied using various methods and including the regime where frustration induces incommensurability. Several improvements are made on the results of the seminal work of Sigrist and Furusaki [J. Phys. Soc. Jpn. 65, 2385 (1996)]. Deviations from the Brillouin magnetic curve due to interactions are also analyzed. First, the magnetic profile around a single impurity and effective interactions between impurities are analyzed within the bond-operator mean-field theory and compared to density-matrix renormalization group calculations. Then, the temperature behavior of the Curie constant is studied in details. At zero-temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattice and compute exactly the distribution of ladder cluster due to chain breaking effects. Using exact diagonalization and quantum Monte-Carlo methods on the effective model, the temperature dependence of the Curie constant is compared to a random dimer model and a real-space renormalization group scenario. Next, the low-part of the magnetic curve corresponding to the contribution of impurities is computed using exact diagonalization. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from the Brillouin response. At zero-temperature, the effective model prediction agrees relatively well with density-matrix renormalization group calculations. Finite-temperature effects are displayed within the effective model and for large depleted ladder models using quantum Monte-Carlo simulations. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu2PO6 compound and other spin-gapped materials are briefly discussed.Comment: 24 pages, 20 figure

Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder

The phase diagram of an antiferromagnetic ladder with frustrating next-nearest neighbor couplings along the legs is determined using numerical methods (exact diagonalization and density-matrix renormalization group) supplemented by strong-coupling and mean-field analysis. Interestingly, this model displays remarkable features, bridging the physics of the J_1-J_2 chain and of the unfrustated ladder. The phase diagram as a function of the transverse coupling J_{\perp} and the frustration J_2 exhibits an Ising transition between a columnar phase of dimers and the usual rung-singlet phase of two-leg ladders. The transition is driven by resonating valence bond fluctuations in the singlet sector while the triplet spin gap remains finite across the transition. In addition, frustration brings incommensurability in the real-space spin correlation functions, the onset of which evolves smoothly from the J_1-J_2 chain value to zero in the large-J_{\perp} limit. The onset of incommensurability in the spin structure-factor and in the dispersion relation is also analyzed. The physics of the frustrated rung-singlet phase is well understood using perturbative expansions and mean-field theories in the large-J_{\perp} limit. Lastly, we discuss the effect of the non-trivial magnon dispersion relation on the thermodynamical properties of the system. The relation of this model and its physics to experimental observations on compounds which are currently investigated, such as BiCu_2PO_6, is eventually addressed.Comment: 13 pages, 13 figure

Spinon excitation spectra of the J1J_1-J2J_2 chain from analytical calculations in the dimer basis and exact diagonalization

11 pages, 6 figuresInternational audienceThe excitation spectrum of the frustrated spin-$1/2$ Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at $J_2=0.25J_1$ and an onset of incommensurability in the dispersion relation at $J_2=9/17J_1$ [as in S. Brehmer \emph{et al.}, J. Phys.: Condens. Matter \textbf{10}, 1103 (1998)]. These analytical results provide a good support for the understanding of exact diagonalization spectra, assuming an independent spinons picture