The Density Matrix Renormalization Group and the Nuclear Shell Model

We summarize recent efforts to develop an angular-momentum-conserving variant of the Density Matrix Renormalization Group method into a practical truncation strategy for large-scale shell model calculations of atomic nuclei. Following a brief description of the key elements of the method, we report the results of test calculations for $^{48}$Cr and $^{56}$Ni. In both cases we consider nucleons limited to the 2p-1f shell and interacting via the KB3 interaction. Both calculations produce a high level of agreement with the exact shell-model results. Furthermore, and most importantly, the fraction of the complete space required to achieve this high level of agreement goes down rapidly as the size of the full space grows

Zeta-like Multizeta Values for higher genus curves

We prove or conjecture several relations between the multizeta values for positive genus function fields of class number one, focusing on the zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or conjecturally equivalently algebraic). These are the first known relations between multizetas, which are not with prime field coefficients. We seem to have one universal family. We also find that interestingly the mechanism with which the relations work is quite different from the rational function field case, raising interesting questions about the expected motivic interpretation in higher genus. We provide some data in support of the guesses.Comment: Expository revisions plus appendices containing proofs of more cases of conjecture

Density Matrix Renormalization Group study of 48^{48}Cr and 56^{56}Ni

We discuss the development of an angular-momentum-conserving variant of the Density Matrix Renormalization Group (DMRG) method for use in large-scale shell-model calculations of atomic nuclei and report a first application of the method to the ground state of $^{56}$Ni and improved results for $^{48}$Cr. In both cases, we see a high level of agreement with the exact results. A comparison of the two shows a dramatic reduction in the fraction of the space required to achieve accuracy as the size of the problem grows.Comment: 4 pages. Published in PRC Rapi