Publications (3)

  • A Schmitt · K-H Mütter · M Karbach
    [Show abstract] [Hide abstract] ABSTRACT: The one-dimensional S = 1 quantum spin chain with a linear and bilinear nearest-neighbour interaction of equal strength is integrable by the nested Bethe ansatz. In this paper the model is studied in the presence of an external magnetic field and an internal crystal field. By solving the Bethe ansatz equations for chains up to length N = 360 we construct the complete phase diagram of the system. We discuss how the magnetization curves depend on the internal field. In the SU(3) phase, where all three densities of atoms with -component -1, 0, +1 are non-vanishing, lines of constant density can be approximately parametrized by modified hypocycloides.
    Article · Jan 1999 · Journal of Physics A General Physics
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    Andreas Schmitt · Karl-Heinz Mütter · Michael Karbach · [...] · Gerhard Müller
    [Show abstract] [Hide abstract] ABSTRACT: The excitation spectra of the T = 0 dynamic structure factors for the spin, dimer, and trimer fluctuation operators as well as for the center fluctuation operator in the one-dimensional S = 1 Heisenberg model with isotropic bilinear (J cos theta) and biquadratic (J sin theta) exchange are investigated via the recursion method for systems with up to N = 18 sites over the predicted range, - pi/4 < theta less than or similar to pi/4, of the topologically ordered Haldane phase. The four static and dynamic structure factors probe the ordering tendencies in the various coupling regimes and the elementary and composite excitations which dominate the T = 0 dynamics. At theta = arctan1/3 (valence-bond solid point), the dynamically relevant spectra in the invariant subspaces with total spin ST = 0,1,2 are dominated by a branch of magnon states (S-T = 1), by continua of two-magnon scattering states (S-T = 0,1,2), and by discrete branches of two-magnon bound states with positive interaction energy (ST = 0,2). The dimer and trimer spectra at q = pi are found to consist of single modes with N-independent excitation energies omega(lambda)(D)//e(0)/ = 5 and omega(lambda)(T)//e(0)/ = 6, where e(0) = E-0/N is the ground-state energy per site. The basic structure of the dynamically relevant excitation spectrum remains the same over a substantial parameter range within the Haldane phase. At the transition to the dimerized phase (theta = - pi/4), the two-magnon excitations turn into two-spinon excitations.
    Full-text available · Article · Sep 1998 · Physical Review B
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    [Show abstract] [Hide abstract] ABSTRACT: In the presence of a uniform field the one-dimensional spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model develops zero frequency excitations at field-dependent 'soft mode' momenta. We determine three types of critical quantities, which we extract from the finite-size dependence of the lowest excitation energies, the singularities in the static structure factors and the infrared singularities in the dynamical structure factors at the soft mode momenta. We also compare our results with the predictions of conformal field theory. Comment: 12 pages, REVTEX, 7 figures, submitted to Physical Review B
    Full-text available · Article · Oct 1996 · Physical review. B, Condensed matter