J. R. Shepard

Dynamic spin response for Heisenberg ladders

We employ the recently proposed plaquette basis to investigate static and dynamic properties of isotropic two-leg Heisenberg spin ladders. Simple noninteracting multiplaquette states provide a remarkably accurate picture of the energy/site and dynamic spin response of these systems. Insights afforded by this simple picture suggest a very efficient truncation scheme for more precise calculations. When the small truncation errors are accounted for using recently developed contractor renormalization techniques, very accurate results requiring a small fraction of the computational effort of exact calculations are obtained. These methods allow us to determine the energy/site, gap, and spin response of 2{times}16 ladders. The former two values are in good agreement with density-matrix renormalization-group results. The spin-response calculations show that nearly all the strength is concentrated in the lowest triplet level and that coherent many-body effects enhance the response/site by nearly a factor of 1.6 over that found for 2{times}2 systems. {copyright} {ital 1998} {ital The American Physical Society}

Three bosons in one dimension with short-range interactions: Zero-range potentials

We consider the three-boson problem with {delta}-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the scattering of one free particle off a bound pair. We first follow a procedure outlined by McGuire in order to obtain an analytic expression for the desired S-matrix element. This result is then compared to a variational calculation in the adiabatic hyperspherical representation, and to a numerical solution to the momentum-space Faddeev equations. We find excellent agreement with the exact phase shifts, and comment on some of the important features in the scattering and bound-state sectors. In particular, we find that the 1+2 scattering length is divergent, marking the presence of a zero-energy resonance which appears as a feature when the pairwise interactions are short range. Finally, we consider the introduction of a three-body interaction, and comment on the cutoff dependence of the coupling.

K+-NUCLEUS QUASIELASTIC SCATTERING

[ital K][sup +]-nucleus quasielastic cross sections measured for a laboratory kaon beam momentum of 705 MeV/[ital c] are presented for 3-momentum transfers of 300 and 500 MeV/[ital c]. The measured differential cross sections for C, Ca, and Pb at 500 MeV/[ital c] are used to deduce the effective number of nucleons participating in the scattering, which are compared with estimates based on the eikonal approximation. The long mean free path expected for [ital K][sup +] mesons in nuclei is found. Double differential cross sections for C and Ca are compared to relativistic nuclear structure calculations.

Scaling functions applied to three-body recombination of Cs-133 atoms

We demonstrate the implications of Efimov physics in the recently measured recombination rate of Cs-133 atoms. By employing previously calculated results for the energy dependence of the recombination rate of He-4 atoms, we obtain three independent scaling functions that are capable of describing the recombination rates over a large energy range for identical bosons with large scattering length. We benchmark these and previously obtained scaling functions by successfully comparing their predictions with full atom-dimer phase shift calculations with artificial He-4 potentials yielding large scattering lengths. Exploiting universality, we finally use these functions to determine the three-body recombination rate of Cs-133 atoms with large positive scattering length, compare our results to experimental data obtained by Kraemer at Innsbruck and find excellent agreement.

Novel Methods for Determining Effective Interactions for the Nuclear Shell Model

The Contractor Renormalization (CORE) method is applied in combination with modern effective-theory techniques to the nuclear many-body problem. A one-dimensional—yet “realistic”—nucleon-nucleon potential is introduced to test these novel ideas. It is found that the magnitude of “model-space” (CORE) corrections diminishes considerably when an effective potential that eliminates the hard-momentum components of the potential is first introduced. As a result, accurate predictions for the ground-state energy of the there-body system are made with relatively little computational effort when both techniques are used in a complementary fashion.

Monte Carlo and renormalization-group effective potentials in scalar field theories.

We study constraint effective potentials for various strongly interacting {phi}{sup 4} theories. Renormalization-group (RG) equations for these quantities are discussed and a heuristic development of a commonly used RG approximation is presented which stresses the relationships among the loop expansion, the Schwinger-Dyson method, and the renormalization-group approach. We extend the standard RG treatment to account explicitly for finite lattice effects. Constraint effective potentials are then evaluated using Monte Carlo (MC) techniques and careful comparisons are made with RG calculations. An explicit treatment of finite lattice effects is found to be essential in achieving quantitive agreement with the MC effective potentials. Excellent agreement is demonstrated for {ital d}=3 and {ital d}=4, O(1) and O(2) cases in both symmetric and broken phases.

Goldstone theorem in the Gaussian functional approximation to the scalarφ 4 theory

We verify the Goldstone theorem in the Gaussian functional approximation to theφ4 theory with internalO(2) symmetry. We do so by reformulating the Gaussian approximation in terms of Schwinger-Dyson equations from which an explicit demonstration of the Goldstone theorem follows directly. Axial current conservation is also shown to hold.

Low-energy operators in effective theories

Modern effective-theory techniques are applied to the nuclear many-body problem. A novel approach is proposed for the renormalization of operators in a manner consistent with the construction of the effective potential. To test this approach, a one-dimensional, yet realistic, nucleon-nucleon potential is introduced. An effective potential is then constructed by tuning its parameters to reproduce the exact effective-range expansion and a variety of bare operators are renormalized in a fashion compatible with this construction. Predictions for the expectation values of these effective operators in the ground state reproduce the results of the exact theory with remarkable accuracy (at the 0.5% level). This represents a marked improvement over a widely practiced approach that uses effective interactions but retains bare operators. Further, it is shown that this improvement is more impressive as the operator becomes more sensitive to the short-range structure of the potential. We illustrate the main ideas of this work using the elastic form factor of the deuteron as an example.

Relativistic nuclear matter with self-consistent correlation energy

We study relativistic nuclear matter in the [sigma]-[omega] model including the ring-sum correlation energy. The model parameters are adjusted self-consistently to give the canonical saturation density and binding energy per nucleon with the ring energy included. Two models are considered, mean-field theory where we neglect vacuum effects, and the relativistic Hartree approximation where such effects are included but in an approximate way. In both cases we find self-consistent solutions and present equations of state. In the mean-field case the ring energy completely dominates the attractive part of the energy density and the elegant saturation mechanism of the standard approach is lost, namely, relativistic quenching of the scalar attraction. In the relativistic Hartree approach the vacuum effects are included in an approximate manner using vertex form factors with a cutoff of 1--2 GeV, the range expected from QCD. Due to the cutoff, the ring energy for this case is significantly smaller, and we obtain self-consistent solutions which preserve the basic saturation mechanism of the standard relativistic approach.

Mean-Field Theory for Spin Ladders Using Angular-Momentum Coupled Bases

We study properties of two-leg Heisenberg spin ladders in a mean-field approximation using a variety of angular-momentum-coupled bases. The mean-field theory proposed by Gopalan, Rice, and Sigrist, which uses a rung basis, assumes that the mean-field ground state consists of a condensate of spin singlets along the rungs of the ladder. We generalize this approach to larger angular-momentum-coupled bases that incorporate{emdash}by their mere definition{emdash}a substantial fraction of the important short-range structure of these materials. In these bases the mean-field ground state remains a condensate of spin singlet{emdash}but now with each involving a larger fraction of the spins in the ladder. As expected, the {open_quotes}purity{close_quotes} of the ground state, as judged by the condensate fraction, increases with the size of the elementary block defining the basis. Moreover, the coupling to quasiparticle excitations becomes weaker as the size of the elementary block increases. Thus, the weak-coupling limit of the theory becomes an accurate representation of the underlying mean-field dynamics. We illustrate the method by computing static and dynamic properties of two-leg ladders in the various angular-momentum-coupled bases. {copyright} {ital 1999} {ital The American Physical Society}