411 research outputs found
Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two- Plus Three-Nucleon Interactions
We formulate the In-Medium Similarity Renormalization Group (IM-SRG) for
open-shell nuclei using a multi-reference formalism based on a generalized Wick
theorem introduced in quantum chemistry. The resulting multi-reference IM-SRG
(MR-IM-SRG) is used to perform the first ab initio study of even oxygen
isotopes with chiral NN and 3N Hamiltonians, from the proton to the neutron
drip lines. We obtain an excellent reproduction of experimental ground-state
energies with quantified uncertainties, which is validated by results from the
Importance-Truncated No-Core Shell Model and the Coupled Cluster method. The
agreement between conceptually different many-body approaches and experiment
highlights the predictive power of current chiral two- and three-nucleon
interactions, and establishes the MR-IM-SRG as a promising new tool for ab
initio calculations of medium-mass nuclei far from shell closures.Comment: 5 pages, 4 figures, v2 corresponding to published versio
First-principles investigations of the magnetic phase diagram of GdCaMnO
We studied for the first time the magnetic phase diagram of the rare-earth
manganites series GdCaMnO (GCMO) over the full
concentration range based on density functional theory. GCMO has been shown to
form solid solutions. We take into account this disordered character by
adapting special quasi random structures at different concentration steps. The
magnetic phase diagram is mainly described by means of the magnetic exchange
interactions between the Mn sites and Monte Carlo simulations were performed to
estimate the corresponding transition temperatures. They agree very well with
recent experiments. The hole doped region shows a strong ferromagnetic
ground state, which competes with A-type antiferromagnetism at higher Ca
concentrations .Comment: Submitted to PR
Modewise Johnson-Lindenstrauss Embeddings for Nuclear Many-Body Theory
In this work, we explore modewise Johnson-Lindenstrauss embeddings (JLEs) as
a tool to reduce the computational cost and memory requirements of nuclear
many-body methods. JLEs are randomized projections of high-dimensional data
tensors onto low-dimensional subspaces that preserve key structural features.
Such embeddings allow for the oblivious and incremental compression of large
tensors, e.g., the nuclear Hamiltonian, into significantly smaller random
sketches that still allow for the accurate calculation of ground-state energies
and other observables. Their oblivious character makes it possible to compress
a tensor without knowing in advance exactly what observables one might want to
approximate at a later time. This opens the door for the use of tensors that
are much too large to store in memory, e.g., complete two-plus three-nucleon
Hamiltonians in large, symmetry-unrestricted bases. Such compressed
Hamiltonians can be stored and used later on with relative ease.
As a first step, we analyze the JLE's impact on the second-order Many-Body
Perturbation Theory (MBPT) corrections for nuclear ground-state observables.
Numerical experiments for a wide range of closed-shell nuclei, model spaces and
state-of-the-art nuclear interactions demonstrate the validity and potential of
the proposed approach: We can compress nuclear Hamiltonians hundred- to
thousand-fold while only incurring mean relative errors of 1\% or less in
ground-state observables. Importantly, we show that JLEs capture the relevant
physical information contained in the highly structured Hamiltonian tensor
despite their random characteristics. In addition to the significant storage
savings, the achieved compressions imply multiple order-of magnitude reductions
in computational effort when the compressed Hamiltonians are used in
higher-order MBPT or nonperturbative many-body methods.Comment: 23 pages, 14 figure
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