14 research outputs found
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Are smooth pseudopotentials a good choice for representing short-range interactions?
Are smooth pseudopotentials a good choice for representing short-range interactions?
When seeking a numerical representation of a quantum-mechanical multiparticle
problem it is tempting to replace a singular short-range interaction by a
smooth finite-range pseudopotential. Finite basis set expansions, e.g.~in Fock
space, are then guaranteed to converge exponentially. The need to faithfully
represent the artificial length scale of the pseudopotential, however, places a
costly burden on the basis set. Here we discuss scaling relations for the
required size of the basis set and demonstrate the basis set convergence on the
example of a two-dimensional system of few fermions with short-range -wave
interactions in a harmonic trapping potential. In particular we show that the
number of harmonic-oscillator basis functions needed to reach a regime of
exponential convergence for a Gaussian pseudopotential scales with the fourth
power of the pseudopotential length scale, which can be improved to quadratic
scaling when the basis functions are re-scaled appropriately. Numerical
examples for three fermions with up to a few hundred single-particle basis
functions are presented and implications for the feasibility of accurate
numerical multi-particle simulations of interacting ultra-cold atom systems are
discussed.Comment: 11 pages, 2 figure
Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions
Exact diagonalization expansions of Bose or Fermi gases with contact
interactions converge very slowly due to a non-analytic cusp in the wave
function. Here we develop a transcorrelated approach where the cusp is treated
exactly and folded into the many-body Hamiltonian with a similarity
transformation that removes the leading order singularity. The resulting
transcorrelated Hamiltonian is not hermitian but can be treated numerically
with a standard projection approach. The smoothness of the wave function
improves by at least one order and thus the convergence rate for the ground
state energy improves. By numerical investigation of a one-dimensional gas of
spin- fermions we find the error in the transcorrelated energy to
scale as with a single-particle basis of plane waves compared to
for the expansion of the original Hamiltonian and using
conventional lattice renormalization
New Strategies in Modeling Electronic Structures and Properties with Applications to Actinides
This chapter discusses contemporary quantum chemical methods and provides
general insights into modern electronic structure theory with a focus on
heavy-element-containing compounds. We first give a short overview of
relativistic Hamiltonians that are frequently applied to account for
relativistic effects. Then, we scrutinize various quantum chemistry methods
that approximate the -electron wave function. In this respect, we will
review the most popular single- and multi-reference approaches that have been
developed to model the multi-reference nature of heavy element compounds and
their ground- and excited-state electronic structures. Specifically, we
introduce various flavors of post-Hartree--Fock methods and optimization
schemes like the complete active space self-consistent field method, the
configuration interaction approach, the Fock-space coupled cluster model, the
pair-coupled cluster doubles ansatz, also known as the antisymmetric product of
1 reference orbital geminal, and the density matrix renormalization group
algorithm. Furthermore, we will illustrate how concepts of quantum information
theory provide us with a qualitative understanding of complex electronic
structures using the picture of interacting orbitals. While modern quantum
chemistry facilitates a quantitative description of atoms and molecules as well
as their properties, concepts of quantum information theory offer new
strategies for a qualitative interpretation that can shed new light onto the
chemistry of complex molecular compounds.Comment: 43 pages, 3 figures, Version of Recor
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Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions
NECI: N-Electron Configuration Interaction with an emphasis on state-of-the-art stochastic methods
We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24 000 central processing unit cores. In this paper, we describe the core functionalities of NECI and its recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green’s functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing us to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs, and it is licensed under GPL-3.0