Cluster expansion for dimerized spin systems

We have studied dimerized spin systems by realizing the cluster expansion to high order. We have extended our previous dimer expansion for one-dimensional systems to cover weakly interacting chains for a quantitative description of three dimensional materials like PHCC and KCuCl_3. By comparison with recent inelastic neutron scattering data we are able to determine the exchange energies between individual spins. We have further investigated the incommensurate region of zigzag chains with isotropic exchange coupling constants near the disorder-line where the dispersion curve exhibits a minimum at a finite wavevector. Our approach clearly shows the gradual transition between the minimum of the dispersion at wavevector 0 and wavevector Pi within this region. The extent of the incommensurate regime is given analytically in an expansion in the coupling constants.Comment: 3 pages, 3 figures; contribution to ICNS2001; uses svjour.clo, svglobal.clo (included

Dynamics of the Distorted Diamond Chain

We present results on the dynamics of the distorted diamond chain, S=1/2 dimers alternating with single spins 1/2 and exchange couplings $J_1$ and $J_3$ in between. The dynamics in the spin fluid (SF) and tetramer-dimer (TD) phases is investigated numerically by exact diagonalisation for up to 24 spins. Representative excitation spectra are presented, both for zero magnetic field and in the 1/3 plateau phase and the relevant parameters are determined across the phase diagram. The behavior across the SF-TD phase transition line is discussed for the specific heat and for excitation spectra. The relevance of the distorted diamond chain model for the material Cu$_3$(CO$_3$)$_2$(OH)$_2$ (azurite) is discussed with particular emphasis on inelastic neutron scattering experiments, a recent suggestion of one possibly ferromagnetic coupling constant is not confirmed.Comment: 24 pages, 8 figure

Response functions of gapped spin systems in high magnetic field

We study the dynamical structure factor of gapped one-dimensional spin systems in the critical phase in high magnetic field. It is shown that the presence of a ``condensate'' in the ground state in the high-field phase leads to interesting signatures in the response functions.Comment: uses ptptex.sty (included), 10 pages, 3 figs, to appear in Prog. Theor. Phys. Suppl. (Proc. of the 16th Nishinomiya Yukawa Memorial Symposium

Finite Temperature Dynamics of the Spin 1/2 Bond Alternating Heisenberg Antiferromagnetic Chain

We present results for the dynamic structure factor of the S=1/2 bond alternating Heisenberg chain over a large range of frequencies and temperatures. Data are obtained from a numerical evaluation of thermal averages based on the calculation of all eigenvalues and eigenfunctions for chains of up to 20 spins. Interpretation is guided by the exact temperature dependence in the noninteracting dimer limit which remains qualitatively valid up to an interdimer exchange $\lambda \approx 0.5$. The temperature induced central peak around zero frequency is clearly identified and aspects of the crossover to spin diffusion in its variation from low to high temperatures are discussed. The one-magnon peak acquires an asymmetric shape with increasing temperature. The two-magnon peak is dominated by the S=1 bound state which remains well defined up to temperatures of the order of J. The variation with temperature and wavevector of the integrated intensity for one and two magnon scattering and of the central peak are discussed.Comment: 8 pages, 8 figure

Ground-state phases of rung-alternated spin-1/2 Heisenberg ladder

The ground-state phase diagram of Heisenberg spin-1/2 system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic Luttinger liquid phase with both linear and quadratic low energy dispersions and ground state magnetization continuously changing with system parameters. For the case of antiferromagnetic exchanges along legs, different dimerized states including states with additional topological order are suggested to be realized