94 research outputs found
Itinerant-electron magnetism: the importance of many-body correlations
Do electrons become ferromagnetic just because of their repulisve Coulomb
interaction? Our calculations on the three-dimensional electron gas imply that
itinerant ferromagnetim of delocalized electrons without lattice and band
structure, the most basic model considered by Stoner, is suppressed due to
many-body correlations as speculated already by Wigner, and a possible
ferromagnetic transition lowering the density is precluded by the formation of
the Wigner crystal.Comment: published version including supplementary materia
Nonlinear Network description for many-body quantum systems in continuous space
We show that the recently introduced iterative backflow renormalization can
be interpreted as a general neural network in continuum space with non-linear
functions in the hidden units. We use this wave function within Variational
Monte Carlo for liquid He in two and three dimensions, where we typically
find a tenfold increase in accuracy over currently used wave functions.
Furthermore, subsequent stages of the iteration procedure define a set of
increasingly good wave functions, each with its own variational energy and
variance of the local energy: extrapolation of these energies to zero variance
gives values in close agreement with the exact values. For two dimensional
He, we also show that the iterative backflow wave function can describe
both the liquid and the solid phase with the same functional form -a feature
shared with the Shadow Wave Function, but now joined by much higher accuracy.
We also achieve significant progress for liquid He in three dimensions,
improving previous variational and fixed-node energies for this very
challenging fermionic system
Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo
We present a simple and general formalism to compute efficiently the
derivatives of a multi-determinant Jastrow-Slater wave function, the local
energy, the interatomic forces, and similar quantities needed in quantum Monte
Carlo. Through a straightforward manipulation of matrices evaluated on the
occupied and virtual orbitals, we obtain an efficiency equivalent to
algorithmic differentiation in the computation of the interatomic forces and
the optimization of the orbital paramaters. Furthermore, for a large
multi-determinant expansion, the significant computational gain recently
reported for the calculation of the wave function is here improved and extended
to all local properties in both all-electron and pseudopotential calculations.Comment: 15 pages, 3 figure
Optimizing the energy with quantum Monte Carlo: A lower numerical scaling for Jastrow-Slater expansions
We present an improved formalism for quantum Monte Carlo calculations of
energy derivatives and properties (e.g. the interatomic forces), with a
multideterminant Jastrow-Slater function. As a function of the number of
Slater determinants, the numerical scaling of per derivative we have
recently reported is here lowered to for the entire set of
derivatives. As a function of the number of electrons , the scaling to
optimize the wave function and the geometry of a molecular system is lowered to
, the same as computing the energy alone in the sampling
process. The scaling is demonstrated on linear polyenes up to CH
and the efficiency of the method is illustrated with the structural
optimization of butadiene and octatetraene with Jastrow-Slater wave functions
comprising as many as 200000 determinants and 60000 parameters
The itinerant ferromagnetic phase of the Hubbard model
Using a newly developed quantum Monte Carlo technique, we provide strong
evidence for the stability of a saturated ferromagnetic phase in the
high-density regime of the two-dimensional infinite-U Hubbard model. By
decreasing the electron density, a discontinuous transition to a paramagnetic
phase is observed, accompanied by a divergence of the susceptibility on the
paramagnetic side. This behavior, resulting from a high degeneracy among
different spin sectors, is consistent with an infinite-order phase transition.
The remarkable stability of itinerant ferromagnetism renews the hope to
describe this phenomenon within a purely kinetic mechanism and will facilitate
the validation of experimental quantum simulators with cold atoms loaded in
optical lattices
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