A Comparative Study of the Magnetization Process of Two-Dimensional Antiferromagnets

Plateaux in the magnetization curves of the square, triangular and hexagonal lattice spin-1/2 XXZ antiferromagnet are investigated. One finds a zero magnetization plateau (corresponding to a spin-gap) on the square and hexagonal lattice with Ising-like anisotropies, and a plateau with one third of the saturation magnetization on the triangular lattice which survives a small amount of easy-plane anisotropy. Here we start with transfer matrix computations for the Ising limit and continue with series in the XXZ-anisotropy for plateau-boundaries using the groundstates of the Ising limit. The main focus is then a numerical computation of the magnetization curves with anisotropies in the vicinity of the isotropic situation. Finally, we discuss the universality class associated to the asymptotic behaviour of the magnetization curve close to saturation, as observed numerically in two and higher dimensions.Comment: 21 pages plain TeX (with macro package included), 7 PostScript figures included using psfig.st

Quantum dimer phases in a frustrated spin ladder: Effective field theory approach and exact diagonalization

The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.Comment: 10 pages RevTex4, 7 figures; final version with some small extensions; to appear in Phys. Rev.

Bound states in weakly disordered spin ladders

We study the appearance of bound states in the spin gap of spin-1/2 ladders induced by weak bond disorder. Starting from the strong-coupling limit, i.e., the limit of weakly coupled dimers, we perform a projection on the single-triplet subspace and derive the position of bound states for the single impurity problem of one modified coupling as well as for small impurity clusters. The case of a finite concentration of impurities is treated with the coherent-potential approximation in the strong-coupling limit and compared with numerical results. Furthermore, we analyze the details in the structure of the density of states and relate their origin to the influence of impurity clusters.Comment: 2 pages, 1 figure. Proceedings of SCES'04, to appear in Physica

Atomic Fermi gas in the trimerized Kagom\'e lattice at the filling 2/3

We study low temperature properties of an atomic spinless interacting Fermi gas in the trimerized Kagom\'e lattice for the case of two fermions per trimer. The system is described by a quantum spin 1/2 model on the triangular lattice with couplings depending on bonds directions. Using exact diagonalizations we show that the system exhibits non-standard properties of a {\it quantum spin-liquid crystal}, combining a planar antiferromagnetic order with an exceptionally large number of low energy excitations.Comment: 4 pages & 4 figures + 2 tables, better version of Fig.

Computing Yukawa Couplings from Magnetized Extra Dimensions

We compute Yukawa couplings involving chiral matter fields in toroidal compactifications of higher dimensional super-Yang-Mills theory with magnetic fluxes. Specifically we focus on toroidal compactifications of D=10 super-Yang-Mills theory, which may be obtained as the low-energy limit of Type I, Type II or Heterotic strings. Chirality is obtained by turning on constant magnetic fluxes in each of the 2-tori. Our results are general and may as well be applied to lower D=6,8 dimensional field theories. We solve Dirac and Laplace equations to find out the explicit form of wavefunctions in extra dimensions. The Yukawa couplings are computed as overlap integrals of two Weyl fermions and one complex scalar over the compact dimensions. In the case of Type IIB (or Type I) string theories, the models are T-dual to (orientifolded) Type IIA with D6-branes intersecting at angles. These theories may have phenomenological relevance since particular models with SM group and three quark-lepton generations have been recently constructed. We find that the Yukawa couplings so obtained are described by Riemann theta-functions, which depend on the complex structure and Wilson line backgrounds. Different patterns of Yukawa textures are possible depending on the values of these backgrounds. We discuss the matching of these results with the analogous computation in models with intersecting D6-branes. Whereas in the latter case a string computation is required, in our case only field theory is needed.Comment: 73 pages, 9 figures. Using JHEP3.cls. Typos and other minor corrections fixed. References adde

Excitation Spectrum and Correlation Functions of the Z_3-Chiral Potts Quantum Spin Chain

We study the excitation spectrum and the correlation functions of the Z_3- chiral Potts model in the massive high-temperature phase using perturbation expansions and numerical diagonalization. We are mainly interested in results for general chiral angles but we consider also the superintegrable case. For the parameter values considered, we find that the band structure of the low- lying part of the excitation spectrum has the form expected from a quasiparticle picture with two fundamental particles. Studying the N-dependence of the spectrum, we confirm the stability of the second fundamental particle in a limited range of the momentum, even when its energy becomes so high that it lies very high up among the multiparticle scattering states. This is not a phenomenon restricted to the superintegrable line. Calculating a non-translationally invariant correlation function, we give evidence that it is oscillating. Within our numerical accuracy we find a relation between the oscillation length and the dip position of the momentum dispersion of the lightest particle which seems to be quite independent of the chiral angles.Comment: 19 pages + 6 PostScript figures (LaTeX); BONN-TH-94-2

Monte Carlo studies of the Ising square lattice with competing interactions

We use improved Monte-Carlo algorithms to study the antiferromagnetic 2D-Ising model with competing interactions $J_1$ on nearest neighbour and $J_2$ on next-nearest neighbour bonds. The finite-temperature phase diagram is divided by a critical point at $J_2 = J_1/2$ where the groundstate is highly degenerate. To analyse the phase boundaries we look at the specific heat and the energy distribution for various ratios of $J_2/J_1$. We find a first order transition for small $J_2 > J_1/2$ and the transition temperature suppressed to $T_C=0$ at the critical point.Comment: 4 pages, 4 figures, accepted for publication in the proceedings of the conference on Highly Frustrated Magnets 2008 in Braunschwei

Magnetocaloric effect in integrable spin-s chains

We study the magnetocaloric effect for the integrable antiferromagnetic high-spin chain. We present an exact computation of the Gr\"uneisen parameter, which is closely related to the magnetocaloric effect, for the quantum spin-s chain on the thermodynamical limit by means of Bethe ansatz techniques and the quantum transfer matrix approach. We have also calculated the entropy S and the isentropes in the (H,T) plane. We have been able to identify the quantum critical points H_c^{(s)}=2/(s+1/2) looking at the isentropes and/or the characteristic behaviour of the Gr\"uneisen parameter.Comment: 6 pages, 3 figure