Impurity Energy Level Within The Haldane Gap

An impurity bond $J{'}$ in a periodic 1D antiferromagnetic, spin 1 chain with exchange $J$ is considered. Using the numerical density matrix renormalization group method, we find an impurity energy level in the Haldane gap, corresponding to a bound state near the impurity bond. When $J{'}<J$ the level changes gradually from the edge of the Haldane gap to the ground state energy as the deviation $dev=(J-J{'})/J$ changes from 0 to 1. It seems that there is no threshold. Yet, there is a threshold when $J{'}>J$. The impurity level appears only when the deviation $dev=(J{'}-J)/J{'}$ is greater than $B_{c}$, which is near 0.3 in our calculation.Comment: Latex file,9 pages uuencoded compressed postscript including 4 figure

The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized $J$-$J'$ model interpolating between both systems by varying $J'/J$ from $J'/J=0$ (bounce limit) to $J'/J=1$ (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the "pure" bounce ($J'/J=0$) and maple-leaf ($J'/J=1$) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range $0 \le J'/J \lesssim J'_c/J$ and that the magnetic order parameter varies only weakly with $J'/J$. At $J'_c \approx 1.45 J$ a direct first-order transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place. The orthogonal-dimer state is the exact ground state in this large-$J'$ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We a find a 1/3 magnetization plateau for $J'/J \gtrsim 1.07$ and another one at 2/3 of saturation emerging only at large $J'/J \gtrsim 3$.Comment: 9 pages, 10 figure

Majorana neutrinos and lepton-number-violating signals in top-quark and W-boson rare decays

We discuss rare lepton-number-violating top-quark and W-boson four-body decays to final states containing a same-charge lepton pair, of the same or of different flavors: t -> b W- li^+ lj^+ and W+ -> J J' li^+ lj^+, where i \ne j or i=j and J J' stands for two light jets originating from a (u-bar d) or a (c-bar s) pair. These \Delta L=2 decays are forbidden in the Standard Model and may be mediated by exchanges of Majorana neutrinos. We adopt a model independent approach for the Majorana neutrinos mixing pattern and calculate the branching ratios (BR) for these decays. We find, for example, that for O(1) mixings between heavy and light Majorana neutrinos (not likely but not ruled out) and if at least one of the heavy Majorana neutrinos has a mass of ~100 GeV, then the BR's for these decays are: BR(t -> b li^+ lj^+ W-) ~ 10^{-4} and BR(W+ -> li^+ lj^+ J J') ~ 10^{-7} if m_N ~ 100 GeV and BR(t -> b li^+ lj^+ J J') ~ BR(W+ -> li^+ lj^+ J J') ~ 0.01 if m_N < 50 GeV. Taking into account the present limits on the neutrino mixing parameters, we obtain more realistic values for these BR's: BR(t -> b li^+ lj^+ W-) ~ 10^{-6} and BR(W+ -> li^+ lj^+ J J') ~ 10^{-10} for m_N ~ 100 GeV and BR(t -> b li^+ lj^+ J J') ~ BR(W+ -> li^+ lj^+ J J') ~ 10^{-6} for m_N < 50 GeV.Comment: latex, 7 pages, 2 figures. V2 as published in PL

Impurity state in Haldane gap for S=1 Heisenberg antiferromagnetic chain with bond doping

Using a new impurity density matrix renormalization group scheme, we establish a reliable picture of how the low lying energy levels of a $S=1$ Heisenberg antiferromagnetic chain change {\it quantitatively} upon bond doping. A new impurity state gradually occurs in the Haldane gap as $J' < J$, while it appears only if $J'/J>\gamma_c$ with $1/\gamma_c=0.708$ as $J'>J$. The system is non-perturbative as $1\leq J'/J\leq\gamma_c$. This explains the appearance of a new state in the Haldane gap in a recent experiment on Y$_{2-x}$Ca$_x$BaNiO$_5$ [J.F. DiTusa, et al., Phys. Rev. Lett. 73 1857(1994)].Comment: 4 pages of uuencoded gzip'd postscrip

Universality in the partially anisotropic three-dimensional Ising lattice

Using transfer-matrix extended phenomenological renormalization-group methods the critical properties of spin-1/2 Ising model on a simple-cubic lattice with partly anisotropic coupling strengths ${\vec J}=(J',J',J)$ are studied. Universality of both fundamental critical exponents $y_t$ and $y_h$ is confirmed. It is shown that the critical finite-size scaling amplitude ratios $U=A_{\chi^{(4)}}A_\kappa/A_\chi^2$, $Y_1=A_{\kappa^{''}}/A_\chi$, and $Y_2=A_{\kappa^{(4)}}/A_{\chi^{(4)}}$ are independent of the lattice anisotropy parameter $\Delta=J'/J$. By this for the last above invariant of the three-dimensional Ising universality class we give the first quantitative estimate: $Y_2\simeq2.013$ (shape $L\times L\times\infty$, periodic boundary conditions in both transverse directions).Comment: 11 pages in latex; no figure

Supersymmetry of Tensionless Rotating Strings in AdS_5 x S^5, and Nearly-BPS Operators

It is shown that a class of rotating strings in AdS_5 x S^5 with SO(6) angular momenta (J,J',J') preserve 1/8-supersymmetry for large J,J', in which limit they are effectively tensionless; when J=0, supersymmetry is enhanced to 1/4. These results imply that recent checks of the AdS/CFT correspondence actually test a nearly-BPS sector.Comment: 12 pages, no figures; v2: new section on CFT operators and new references added, discussion section and acknowledgements modified, abstract rephrashe