Comment on ``Density-matrix renormalization-group method for excited states''

In a Physical Review B paper Chandross and Hicks claim that an analysis of the density-density correlation function in the dimerised Hubbard model of polyacetylene indicates that the optical exciton is bound, and that a previous study by Boman and Bursill that concluded otherwise was incorrect due to numerical innacuracy. We show that the method used in our original paper was numerically sound and well established in the literature. We also show that, when the scaling with lattice size is analysed, the interpretation of the density-density correlation function adopted by Chandross and Hicks in fact implies that the optical exciton is unbound.Comment: RevTeX, 10 pages, 4 eps figures fixed and included now in tex

Learning Together: Using Action Research to Design Professional Development

After being part of a week-long math institute, both the principal and the Mathematics Specialist from an urban school district partnered to develop a professional development plan. It incorporated a Lesson Study Model that supported collaborative learning teams, focused on the instructional process, and incorporated reflection and feedback. Although the faculty had engaged in other forms of professional development, the lesson study process was seen as a powerful vehicle that invited a level of coaching and cross-collaboration. This article focuses on the shared viewpoints of the principal and the Mathematics Specialist who worked together to build a mechanism for professional learning for improved mathematical proficiency and understanding

Energetics of Domain Walls in the 2D t-J model

Using the density matrix renormalization group, we calculate the energy of a domain wall in the 2D t-J model as a function of the linear hole density \rho_\ell, as well as the interaction energy between walls, for J/t=0.35. Based on these results, we conclude that the ground state always has domain walls for dopings 0 < x < 0.3. For x < 0.125, the system has (1,0) domain walls with \rho_\ell ~ 0.5, while for 0.125 < x < 0.17, the system has a possibly phase-separated mixture of walls with \rho_\ell ~ 0.5 and \rho_\ell =1. For x > 0.17, there are only walls with \rho_\ell =1. For \rho_\ell = 1, diagonal (1,1) domain walls have very nearly the same energy as (1,0) domain walls.Comment: Several minor changes. Four pages, four encapsulated figure

Spin Gaps in a Frustrated Heisenberg model for CaV4_4O9_9

I report results of a density matrix renormalization group (DMRG) study of a model for the two dimensional spin-gapped system CaV$_4$O$_9$. This study represents the first time that DMRG has been used to study a two dimensional system on large lattices, in this case as large as $24\times 11$, allowing extrapolation to the thermodynamic limit. I present a substantial improvement to the DMRG algorithms which makes these calculations feasible.Comment: 10 pages, with 4 Postscript figure

Effect of the W-term for a t-U-W Hubbard ladder

Antiferromagnetic and d_{x2-y2}-pairing correlations appear delicately balanced in the 2D Hubbard model. Whether doping can tip the balance to pairing is unclear and models with additional interaction terms have been studied. In one of these, the square of a local hopping kinetic energy H_W was found to favor pairing. However, such a term can be separated into a number of simpler processes and one would like to know which of these terms are responsible for enhancing the pairing. Here we analyze these processes for a 2-leg Hubbard ladder

The High Energy Behavior of the Forward Scattering Parameters---An Amplitude Analysis Update

Utilizing the most recent experimental data, we reanalyze high energy \pbar p and pp data, using the asymptotic amplitude analysis, under the assumption that we have reached `asymptopia'. This analysis gives strong evidence for a $\log \,(s/s_0)$ dependence at {\em current} energies and {\em not} $\log^2 (s/s_0)$, and also demonstrates that odderons are {\em not} necessary to explain the experimental data.Comment: 7 pages in LaTeX, 4 figures and 5 files, uuencoded in file "sigall.uu