In-Medium Similarity Renormalization Group for Nuclei

We present a new ab-initio method that uses similarity renormalization group (SRG) techniques to continuously diagonalize nuclear many-body Hamiltonians. In contrast with applications of the SRG to two- and three-nucleon interactions in free space, we perform the SRG evolution "in medium" directly in the $A$-body system of interest. The in-medium approach has the advantage that one can approximately evolve $3,...,A$-body operators using only two-body machinery based on normal-ordering techniques. The method is nonperturbative and can be tailored to problems ranging from the diagonalization of closed-shell nuclei to the construction of effective valence shell-model Hamiltonians and operators. We present first results for the ground-state energies of $^4$He, $^{16}$O and $^{40}$Ca, which have accuracies comparable to coupled-cluster calculations.Comment: 4pages, 4 figures, to be published in PR

High-gradient operators in the N-vector model

It has been shown by several authors that a certain class of composite operators with many fields and gradients endangers the stability of nontrivial fixed points in 2+eps expansions for various models. This problem is so far unresolved. We investigate it in the N-vector model in an 1/N-expansion. By establishing an asymptotic naive addition law for anomalous dimensions we demonstrate that the first orders in the 2+eps expansion can lead to erroneous interpretations for high--gradient operators. While this makes us cautious against over--interpreting such expansions (either 2+eps or 1/N), the stability problem in the N-vector model persists also in first order in 1/N below three dimensions.Comment: 18 pages, 4 Postscript figures; revised version contains two additional references and "Note added in proof

Flow equation solution for the weak to strong-coupling crossover in the sine-Gordon model

A continuous sequence of infinitesimal unitary transformations, combined with an operator product expansion for vertex operators, is used to diagonalize the quantum sine-Gordon model for 2 pi < beta^2 < infinity. The leading order of this approximation already gives very accurate results for the single-particle gap in the strong-coupling phase. This approach can be understood as an extension of perturbative scaling theory since it links weak to strong-coupling behavior in a systematic expansion. The approach should also be useful for other strong-coupling problems that can be formulated in terms of vertex operators.Comment: 4 pages, 1 figure, minor changes (typo in Eq. (3) corrected, references added), published versio

Block Diagonalization using SRG Flow Equations

By choosing appropriate generators for the Similarity Renormalization Group (SRG) flow equations, different patterns of decoupling in a Hamiltonian can be achieved. Sharp and smooth block-diagonal forms of phase-shift equivalent nucleon-nucleon potentials in momentum space are generated as examples and compared to analogous low-momentum interactions ("v_lowk").Comment: 4 pages, 9 figures (pdfLaTeX

Local Projections of Low-Momentum Potentials

Nuclear interactions evolved via renormalization group methods to lower resolution become increasingly non-local (off-diagonal in coordinate space) as they are softened. This inhibits both the development of intuition about the interactions and their use with some methods for solving the quantum many-body problem. By applying "local projections", a softened interaction can be reduced to a local effective interaction plus a non-local residual interaction. At the two-body level, a local projection after similarity renormalization group (SRG) evolution manifests the elimination of short-range repulsive cores and the flow toward universal low-momentum interactions. The SRG residual interaction is found to be relatively weak at low energy, which motivates a perturbative treatment

In-Medium Similarity Renormalization Group with Chiral Two- Plus Three-Nucleon Interactions

We use the recently proposed In-Medium Similarity Renormalization Group (IM-SRG) to carry out a systematic study of closed-shell nuclei up to \nuc{Ni}{56}, based on chiral two- plus three-nucleon interactions. We analyze the capabilities of the IM-SRG by comparing our results for the ground-state energy to Coupled Cluster calculations, as well as to quasi-exact results from the Importance-Truncated No-Core Shell Model. Using chiral two- plus three-nucleon Hamiltonians whose resolution scales are lowered by free-space SRG evolution, we obtain good agreement with experimental binding energies in \nuc{He}{4} and the closed-shell oxygen isotopes, while the calcium and nickel isotopes are somewhat overbound.Comment: 11 pages, 7 figures, submitted to Phys. Rev.

Symmetric Anderson impurity model with a narrow band

The single channel Anderson impurity model is a standard model for the description of magnetic impurities in metallic systems. Usually, the bandwidth represents the largest energy scale of the problem. In this paper, we analyze the limit of a narrow band, which is relevant for the Mott-Hubbard transition in infinite dimensions. For the symmetric model we discuss two different effects: i) The impurity contribution to the density of states at the Fermi surface always turns out to be negative in such systems. This leads to a new crossover in the thermodynamic quantities that we investigate using the numerical renormalization group. ii) Using the Lanczos method, we calculate the impurity spectral function and demonstrate the breakdown of the skeleton expansion on an intermediate energy scale. Luttinger's theorem, as an example of the local Fermi liquid property of the model, is shown to still be valid.Comment: 4 pages RevTeX, 2 eps figures included, final versio

Flow equations for Hamiltonians: Contrasting different approaches by using a numerically solvable model

To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered which is structurally similar to impurity models. By this we discuss the question of optimization for the first time. A general truncation scheme is established that produces good results for the Hamiltonian flow as well as for the operator flow. Nevertheless, it is also pointed out that a systematic and feasible scheme for the operator flow on the operator level is missing. For this, an explicit analysis of the operator flow is given for the first time. We observe that truncation of the series of the observable flow after the linear or bilinear terms does not yield satisfactory results for the entire parameter regime as - especially close to resonances - even high orders of the exact series expansion carry considerable weight.Comment: 25 pages, 10 figure

Decoupling in the Similarity Renormalization Group for Nucleon-Nucleon Forces

Decoupling via the Similarity Renormalization Group (SRG) of low-energy nuclear physics from high-energy details of the nucleon-nucleon interaction is examined for two-body observables and few-body binding energies. The universal nature of this decoupling is illustrated and errors from suppressing high-momentum modes above the decoupling scale are shown to be perturbatively small.Comment: 13 pages, 14 figure

Assisted hopping and interaction effects in impurity models

We study, using Numerical Renormalization Group methods, the generalization of the Anderson impurity model where the hopping depends on the filling of the impurity. We show that the model, for sufficiently large values of the assisted hopping term, shows a regime where local pairing correlations are enhanced. These correlations involve pairs fluctuating between on site and nearest neighbor positions