Effect of a Spin-1/2 Impurity on the Spin-1 Antiferromagnetic Heisenberg Chain

Low-lying excited states as well as the ground state of the spin-1 antiferro- magnetic Heisenberg chain with a spin-1/2 impurity are investigated by means of a variational method and a method of numerical diagonalization. It is shown that 1) the impurity spin brings about massive modes in the Haldane gap, 2) when the the impurity-host coupling is sufficiently weak, the phenomenological Hamiltonian used by Hagiwara {\it et al.} in the analysis of ESR experimental results for NENP containing a small amount of spin-1/2 Cu impurities is equivalent to a more realistic Hamiltonian, as far as the energies of the low-lying states are concerned, 3) the results obtained by the variational method are in semi-quantitatively good agreement with those obtained by the numerical diagonalization.Comment: 11 pages, plain TeX (Postscript figures are included), KU-CCS-93-00

Planet formation around low mass stars: the moving snow line and super-Earths

We develop a semi-analytic model for planet formation during the pre-main sequence contraction phase of a low mass star. During this evolution, the stellar magnetosphere maintains a fixed ratio between the inner disk radius and the stellar radius. As the star contracts at constant effective temperature, the `snow line', which separates regions of rocky planet formation from regions of icy planet formation, moves inward. This process enables rapid formation of icy protoplanets that collide and merge into super-Earths before the star reaches the main sequence. The masses and orbits of these super-Earths are consistent with super-Earths detected in recent microlensing experiments.Comment: accepted by ApJ Letter

Solitonic excitations in the Haldane phase of a S=1 chain

We study low-lying excitations in the 1D $S=1$ antiferromagnetic valence-bond-solid (VBS) model. In a numerical calculation on finite systems the lowest excitations are found to form a discrete triplet branch, separated from the higher-lying continuum. The dispersion of these triplet excitations can be satisfactorily reproduced by assuming approximate wave functions. These wave functions are shown to correspond to moving hidden domain walls, i.e. to one-soliton excitations.Comment: RevTex 3.0, 24 pages, 2 figures on request by fax or mai

Connectivity transition in the frustrated S=1 chain revisited

The phase transition in the antiferromagnetic isotropic Heisenberg S=1 chain with frustrating next-nearest neighbor coupling alpha is reconsidered. We identify the order parameter of the large-alpha phase as describing two intertwined strings, each possessing a usual string order. The transition has a topological nature determined by the change in the string connectivity. Numerical evidence from the DMRG results is supported by the effective theory based on soliton states.Comment: 4 pages, 2 figures, Revtex 4, submitted to PR

Fabrication and properties of gallium phosphide variable colour displays

The unique properties of single-junction gallium phosphide devices incorporating both red and green radiative recombination centers were investigated in application to the fabrication of monolithic 5 x 7 displays capable of displaying symbolic and alphanumeric information in a multicolor format. A number of potentially suitable material preparation techniques were evaluated in terms of both material properties and device performance. Optimum results were obtained for double liquid-phase-epitaxial process in which an open-tube dipping technique was used for n-layer growth and a sealed tipping procedure for subsequent p-layer growth. It was demonstrated that to prepare devices exhibiting a satisfactory range of dominant wavelengths which can be perceived as distinct emission colors extending from the red through green region of the visible spectrum involves a compromise between the material properties necessary for efficient red emission and those considered optimum for efficient green emission

Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain

The density matrix renormalization group (``DMRG'') discovered by White has shown to be a powerful method to understand the properties of many one dimensional quantum systems. In the case where renormalization eventually converges to a fixed point we show that quantum states in the thermodynamic limit with periodic boundary conditions can be simply represented by a special type of product ground state with a natural description of Bloch states of elementary excitations that are spin-1 solitons. We then observe that these states can be rederived through a simple variational ansatz making no reference to a renormalization construction. The method is tested on the spin-1 Heisenberg model.Comment: 13 pages uuencoded compressed postscript including figure

Numerical Study of the S=1S=1 Antiferrromagnetic Spin Chain with Bond Alternation

We study the $S=1$ quantum spin chain with bond alternation {\cal H}=\sum _i (1-(-1)^i\delta)\vect{S}_i\cdot \vect{S}_{i+1} by the density matrix renormalization group method recently proposed by Steven R. White (\PRL{69}{3844}{1993}). We find a massless point at $\delta _c =0.25 \pm 0.01$. We also find the edge states in the region $\delta <\delta_c$ under the open boundary condition, which disappear in the region $\delta >\delta _{c}$. At the massless point, the spin wave velocity $v_s$ is $3.66 \pm 0.10$ and the central charge $c$ is $1.0\pm 0.15$. Our results indicate that a continuous phase transition occurs at the massless point $\delta =\delta_c$ accompanying breaking of the hidden $Z_2\times Z_2$ symmetry.Comment: 9 pages and 1 PostScript figure, Revtex 3.0 (Minor corrections in TEX-file format to remove possible compilatory troubles.

Investigations of Pairing in Anyon Systems

We investigate pairing instabilities in the Fermi-liquid-like state of a single species of anyons. We describe the anyons as Fermions interacting with a Chern-Simons gauge field and consider the weak coupling limit where their statistics approaches that of Fermions. We show that, within the conventional BCS approach, due to induced repulsive Coulomb and current-current interactions, the attractive Aharonov-Bohm interaction is not sufficient to generate a gap in the Fermion spectrum.Comment: (11 pages, 2 Figures not included

New exact solution of the one dimensional Dirac Equation for the Woods-Saxon potential within the effective mass case

We study the one-dimensional Dirac equation in the framework of a position dependent mass under the action of a Woods-Saxon external potential. We find that constraining appropriately the mass function it is possible to obtain a solution of the problem in terms of the hypergeometric function. The mass function for which this turns out to be possible is continuous. In particular we study the scattering problem and derive exact expressions for the reflection and transmission coefficients which are compared to those of the constant mass case. For the very same mass function the bound state problem is also solved, providing a transcendental equation for the energy eigenvalues which is solved numerically.Comment: Version to match the one which has been accepted for publication by J. Phys. A: Math. Theor. Added one figure, several comments and few references. (24 pages and 7 figures

The superconducting phase transition and gauge dependence

The gauge dependence of the renormalization group functions of the Ginzburg-Landau model is investigated. The analysis is done by means of the Ward-Takahashi identities. After defining the local superconducting order parameter, it is shown that its exponent $\beta$ is in fact gauge independent. This happens because in $d=3$ the Landau gauge is the only gauge having a physical meaning, a property not shared by the four-dimensional model where any gauge choice is possible. The analysis is done in both the context of the $\epsilon$-expansion and in the fixed dimension approach. It is pointed out the differences that arise in both of these approaches concerning the gauge dependence.Comment: RevTex, 3 pages, no figures; accepted for publication in PRB; this paper is a short version of cond-mat/990527