Jordan-Wigner approach to the frustrated spin one-half XXZ chain

The Jordan-Wigner transformation is applied to study the ground state properties and dimerization transition in the $J_1-J_2$ $XXZ$ chain. We consider different solutions of the mean-field approximation for the transformed Hamiltonian. Ground state energy and the static structure factor are compared with complementary exact diagonalization and good agreement is found near the limit of the Majumdar-Ghosh model. Furthermore, the ground state phase diagram is discussed within the mean-field theory. In particular, we show that an incommensurate ground state is absent for large $J_2$ in a fully self-consistent mean-field analysis.Comment: final version to appear in Eur. Phys. J. B; 5 pages including 4 figures; some small extensions including additional reference

Transport in quasi one-dimensional spin-1/2 systems

We present numerical results for the spin and thermal conductivity of one-dimensional (1D) quantum spin systems. We contrast the properties of integrable models such as the spin-1/2 XXZ chain against nonintegrable ones such as frustrated and dimerized chains. The thermal conductivity of the XXZ chain is ballistic at finite temperatures, while in the nonintegrable models, this quantity is argued to vanish. For the case of frustrated and dimerized chains, we discuss the frequency dependence of the transport coefficients. Finally, we give an overview over related theoretical work on intrinsic and extrinsic scattering mechanisms of quasi-1D spin systems.Comment: 11 pages, 7 figure

Coset Realization of Unifying W-Algebras

We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and sl(2,R)+sl(2,R) / sl(2,R), and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying W-algebras of Casimir W-algebras. We show that it is possible to give coset realizations of various types of unifying W-algebras, e.g. the diagonal cosets based on the symplectic Lie algebras sp(2n) realize the unifying W-algebras which have previously been introduced as `WD_{-n}'. In addition, minimal models of WD_{-n} are studied. The coset realizations provide a generalization of level-rank-duality of dual coset pairs. As further examples of finitely nonfreely generated quantum W-algebras we discuss orbifolding of W-algebras which on the quantum level has different properties than in the classical case. We demonstrate in some examples that the classical limit according to Bowcock and Watts of these nonfreely finitely generated quantum W-algebras probably yields infinitely nonfreely generated classical W-algebras.Comment: 60 pages (plain TeX) (final version to appear in Int. J. Mod. Phys. A; several minor improvements and corrections - for details see beginning of file

Comment on "Anomalous Thermal Conductivity of Frustrated Heisenberg Spin Chains and Ladders"

In a recent letter [Phys. Rev. Lett. 89, 156603 (2002); cond-mat/0201300], Alvarez and Gros have numerically analyzed the Drude weight for thermal transport in spin ladders and frustrated chains of up to 14 sites and have proposed that it remains finite in the thermodynamic limit. In this comment, we argue that this conclusion cannot be sustained if the finite-size analysis is taken to larger system sizes.Comment: One page REVTeX4, 1 figure. Published version (minor changes

Magnetism of a tetrahedral cluster-chain

Magnetic properties of a completely frustrated tetrahedral chain are briefly summarized. Using exact diagonalization, and bond-operator theory results for the ground-state phase diagram, the one-triplet excitations and the Raman spectrum are given. The link to novel tellurate materials is clarified.Comment: 2 pages, 3 figure

New N=1 Extended Superconformal Algebras with Two and Three Generators

In this paper we consider extensions of the super Virasoro algebra by one and two super primary fields. Using a non-explicitly covariant approach we compute all SW-algebras with one generator of dimension up to 7 in addition to the super Virasoro field. In complete analogy to W-algebras with two generators most results can be classified using the representation theory of the super Virasoro algebra. Furthermore, we find that the SW(3/2, 11/2)-algebra can be realized as a subalgebra of SW(3/2, 5/2) at c = 10/7. We also construct some new SW-algebras with three generators, namely SW(3/2, 3/2, 5/2), SW(3/2, 2, 2) and SW(3/2, 2, 5/2).Comment: 30 pages (Plain TeX), BONN-HE-92-0

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