27 research outputs found
Correlation Induced Inhomogeneity in Circular Quantum Dots
Properties of the "electron gas" - in which conduction electrons interact by
means of Coulomb forces but ionic potentials are neglected - change
dramatically depending on the balance between kinetic energy and Coulomb
repulsion. The limits are well understood. For very weak interactions (high
density), the system behaves as a Fermi liquid, with delocalized electrons. In
contrast, in the strongly interacting limit (low density), the electrons
localize and order into a Wigner crystal phase. The physics at intermediate
densities, however, remains a subject of fundamental research. Here, we study
the intermediate-density electron gas confined to a circular disc, where the
degree of confinement can be tuned to control the density. Using accurate
quantum Monte Carlo techniques, we show that the electron-electron correlation
induced by an increase of the interaction first smoothly causes rings, and then
angular modulation, without any signature of a sharp transition in this density
range. This suggests that inhomogeneities in a confined system, which exist
even without interactions, are significantly enhanced by correlations.Comment: final version, modified introduction and clarifications, 4 page
Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory.
We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 2016, 12, 3674], by introducing a semistochastic algorithm for performing multireference Epstein-Nesbet perturbation theory, in order to completely eliminate the severe memory bottleneck of the original method. The proposed algorithm has several attractive features. First, there is no sign problem that plagues several quantum Monte Carlo methods. Second, instead of using Metropolis-Hastings sampling, we use the Alias method to directly sample determinants from the reference wave function, thus avoiding correlations between consecutive samples. Third, in addition to removing the memory bottleneck, semistochastic HCI (SHCI) is faster than the deterministic variant for many systems if a stochastic error of 0.1 mHa is acceptable. Fourth, within the SHCI algorithm one can trade memory for a modest increase in computer time. Fifth, the perturbative calculation is embarrassingly parallel. The SHCI algorithm extends the range of applicability of the original algorithm, allowing us to calculate the correlation energy of very large active spaces. We demonstrate this by performing calculations on several first row dimers including F2 with an active space of (14e, 108o), Mn-Salen cluster with an active space of (28e, 22o), and Cr2 dimer with up to a quadruple-ζ basis set with an active space of (12e, 190o). For these systems we were able to obtain better than 1 mHa accuracy with a wall time of merely 55 s, 37 s, and 56 min on 1, 1, and 4 nodes, respectively.S.S. acknowledges the startup package from the University of Colorado. A.A.H. and C.J.U. were supported in part by NSF Grant ACI-1534965
Warming Up Density Functional Theory
Density functional theory (DFT) has become the most popular approach to
electronic structure across disciplines, especially in material and chemical
sciences. Last year, at least 30,000 papers used DFT to make useful predictions
or give insight into an enormous diversity of scientific problems, ranging from
battery development to solar cell efficiency and far beyond. The success of
this field has been driven by usefully accurate approximations based on known
exact conditions and careful testing and validation. In the last decade,
applications of DFT in a new area, warm dense matter, have exploded. DFT is
revolutionizing simulations of warm dense matter including applications in
controlled fusion, planetary interiors, and other areas of high energy density
physics. Over the past decade or so, molecular dynamics calculations driven by
modern density functional theory have played a crucial role in bringing
chemical realism to these applications, often (but not always) with excellent
agreement with experiment. This chapter summarizes recent work from our group
on density functional theory at non-zero temperatures, which we call thermal
DFT. We explain the relevance of this work in the context of warm dense matter,
and the importance of quantum chemistry to this regime. We illustrate many
basic concepts on a simple model system, the asymmetric Hubbard dimer
Exact exchange-correlation potential of a ionic Hubbard model with a free surface
We use Lanczos exact diagonalization to compute the exact
exchange-correlation (xc) potential of a Hubbard chain with large binding
energy ("the bulk") followed by a chain with zero binding energy ("the
vacuum"). Several results of density functional theory in the continuum
(sometimes controversial) are verified in the lattice. In particular we show
explicitly that the fundamental gap is given by the gap in the Kohn-Sham
spectrum plus a contribution due to the jump of the xc-potential when a
particle is added. The presence of a staggered potential and a nearest-neighbor
interaction V allows to simulate a ionic solid. We show that in the ionic
regime in the small hopping amplitude limit the xc-contribution to the gap
equals V, while in the Mott regime it is determined by the Hubbard U
interaction. In addition we show that correlations generates a new potential
barrier at the surface
Carbon nanotubes as excitonic insulators
Fifty years ago Walter Kohn speculated that a zero-gap semiconductor might be unstable against the spontaneous generation of excitons-electron-hole pairs bound together by Coulomb attraction. The reconstructed ground state would then open a gap breaking the symmetry of the underlying lattice, a genuine consequence of electronic correlations. Here we show that this excitonic insulator is realized in zero-gap carbon nanotubes by performing first-principles calculations through many-body perturbation theory as well as quantum Monte Carlo. The excitonic order modulates the charge between the two carbon sublattices opening an experimentally observable gap, which scales as the inverse of the tube radius and weakly depends on the axial magnetic field. Our findings call into question the Luttinger liquid paradigm for nanotubes and provide tests to experimentally discriminate between excitonic and Mott insulators
Relationship of Kohn-Sham eigenvalues to excitation energies
In Kohn-Sham density functional theory, only the highest occupied eigenvalue has a rigorous physical meaning, viz., it is the negative of the lowest ionization energy. Here, we demonstrate that for finite systems, the unoccupied true Kohn-Sham eigenvalues las opposed to the those obtained from the commonly used approximate density functionals) are also meaningful in that good approximations to excitation energies can be obtained from them. We argue that the explanation for this observed behavior is that, at large distances, the Kohn-Sham orbitals and the quasiparticle amplitudes satisfy the same equation to order 1/r(4). (C) 1998 Elsevier Science B.V. All rights reserved
Constrained Path Monte Carlo for Fermions
In these lectures we describe the constrained path Monte Carlo (CPMC