Shell Model Monte Carlo studies of neutron-rich nuclei in the 1s-0d-1p-0f shells

We demonstrate the feasibility of realistic Shell-Model Monte Carlo (SMMC) calculations spanning multiple major shells, using a realistic interaction whose bad saturation and shell properties have been corrected by a newly developed general prescription. Particular attention is paid to the approximate restoration of translational invariance. The model space consists of the full sd-pf shells. We include in the study some well-known T=0 nuclei and several unstable neutron-rich ones around N=20,28. The results indicate that SMMC can reproduce binding energies, B(E2) transitions, and other observables with an interaction that is practically parameter free. Some interesting insight is gained on the nature of deep correlations. The validity of previous studies is confirmed.Comment: 22 pages + 7 postscript figure

Random Matrices and the Convergence of Partition Function Zeros in Finite Density QCD

We apply the Glasgow method for lattice QCD at finite chemical potential to a schematic random matrix model (RMM). In this method the zeros of the partition function are obtained by averaging the coefficients of its expansion in powers of the chemical potential. In this paper we investigate the phase structure by means of Glasgow averaging and demonstrate that the method converges to the correct analytically known result. We conclude that the statistics needed for complete convergence grows exponentially with the size of the system, in our case, the dimension of the Dirac matrix. The use of an unquenched ensemble at $\mu=0$ does not give an improvement over a quenched ensemble. We elucidate the phenomenon of a faster convergence of certain zeros of the partition function. The imprecision affecting the coefficients of the polynomial in the chemical potential can be interpeted as the appearance of a spurious phase. This phase dominates in the regions where the exact partition function is exponentially small, introducing additional phase boundaries, and hiding part of the true ones. The zeros along the surviving parts of the true boundaries remain unaffected.Comment: 17 pages, 14 figures, typos correcte

Making chiral fermion actions (almost) gauge invariant using Laplacian gauge fixing

Straight foreward lattice descriptions of chiral fermions lead to actions that break gauge invariance. I describe a method to make such actions gauge invariant (up to global gauge transformations) with the aid of gauge fixing. To make this prescription unambiguous, Laplacian gauge fixing is used, which is free from Gribov ambiguities.Comment: 3 p., Latex, (proc. Lattice '93, Dallas), 2 figs. appended, UCSD/PTH 93-4

Reviving the Method of Particular Solutions

Fox, Henrici and Moler made famous a "Method of Particular Solutions" for computing eigenvalues and eigenmodes of the Laplacian in planar regions such as polygons. We explain why their formulation of this method breaks down when applied to regions that are insufficiently simple and propose a modification that avoids these difficulties. The crucial changes are to introduce points in the interior of the region as well as on the boundary and to minimize a subspace angle rather than just a singular value or a determinant

Fusion in Fractional Level sl^(2)-Theories with k=-1/2

The fusion rules of conformal field theories admitting an sl^(2)-symmetry at level k=-1/2 are studied. It is shown that the fusion closes on the set of irreducible highest weight modules and their images under spectral flow, but not when "highest weight" is replaced with "relaxed highest weight". The fusion of the relaxed modules, necessary for a well-defined u^(1)-coset, gives two families of indecomposable modules on which the Virasoro zero-mode acts non-diagonalisably. This confirms the logarithmic nature of the associated theories. The structures of the indecomposable modules are completely determined as staggered modules and it is shown that there are no logarithmic couplings (beta-invariants). The relation to the fusion ring of the c=-2 triplet model and the implications for the beta gamma ghost system are briefly discussed.Comment: 33 pages, 8 figures; v2 - added a ref and deleted a paragraph from the conclusion