19,814 research outputs found
Multicriticality of the (2+1)-dimensional gonihedric model: A realization of the (d,m)=(3,2) Lifshitz point
Multicriticality of the gonihedric model in 2+1 dimensions is investigated
numerically. The gonihedric model is a fully frustrated Ising magnet with the
finely tuned plaquette-type (four-body and plaquette-diagonal) interactions,
which cancel out the domain-wall surface tension. Because the
quantum-mechanical fluctuation along the imaginary-time direction is simply
ferromagnetic, the criticality of the (2+1)-dimensional gonihedric model should
be an anisotropic one; that is, the respective critical indices of real-space
(\perp) and imaginary-time (\parallel) sectors do not coincide. Extending the
parameter space to control the domain-wall surface tension, we analyze the
criticality in terms of the crossover (multicritical) scaling theory. By means
of the numerical diagonalization for the clusters with N\le 28 spins, we
obtained the correlation-length critical indices
(\nu_\perp,\nu_\parallel)=(0.45(10),1.04(27)), and the crossover exponent
\phi=0.7(2). Our results are comparable to
(\nu_{\perp},\nu_{\parallel})=(0.482,1.230), and \phi=0.688 obtained by Diehl
and Shpot for the (d,m)=(3,2) Lifshitz point with the \epsilon-expansion method
up to O(\epsilon^2)
Many-body localization edge in the random-field Heisenberg chain
We present a large scale exact diagonalization study of the one dimensional
spin Heisenberg model in a random magnetic field. In order to access
properties at varying energy densities across the entire spectrum for system
sizes up to spins, we use a spectral transformation which can be applied
in a massively parallel fashion. Our results allow for an energy-resolved
interpretation of the many body localization transition including the existence
of an extensive many-body mobility edge. The ergodic phase is well
characterized by Gaussian orthogonal ensemble statistics, volume-law
entanglement, and a full delocalization in the Hilbert space. Conversely, the
localized regime displays Poisson statistics, area-law entanglement and non
ergodicity in the Hilbert space where a true localization never occurs. We
perform finite size scaling to extract the critical edge and exponent of the
localization length divergence.Comment: 4+3 pages, 5+3 figure
Time-dependent local Green's operator and its applications to manganites
An algorithm is presented to calculate the electronic local time-dependent
Green's operator for manganites-related hamiltonians. This algorithm is proved
to scale with the number of states in the Hilbert-space to the 1.55 power,
is able of parallel implementation, and outperforms computationally the Exact
Diagonalization (ED) method for clusters larger than 64 sites (using
parallelization). This method together with the Monte Carlo (MC) technique is
used to derive new results for the manganites phase diagram for the spatial
dimension D=3 and half-filling on a 12x12x12 cluster (3456 orbitals). We obtain
as a function of an insulating parameter, the sequence of ground states given
by: ferromagnetic (FM), antiferromagnetic AF-type A, AF-type CE, dimer and
AF-type G, which are in remarkable agreement with experimental results.Comment: 9 pages, 11 figure
Parallel Self-Consistent-Field Calculations via Chebyshev-Filtered Subspace Acceleration
Solving the Kohn-Sham eigenvalue problem constitutes the most computationally
expensive part in self-consistent density functional theory (DFT) calculations.
In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace
iteration method, which avoids computing explicit eigenvectors except at the
first SCF iteration. The method may be viewed as an approach to solve the
original nonlinear Kohn-Sham equation by a nonlinear subspace iteration
technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue
problem. It reaches self-consistency within a similar number of SCF iterations
as eigensolver-based approaches. However, replacing the standard
diagonalization at each SCF iteration by a Chebyshev subspace filtering step
results in a significant speedup over methods based on standard
diagonalization. Here, we discuss an approach for implementing this method in
multi-processor, parallel environment. Numerical results are presented to show
that the method enables to perform a class of highly challenging DFT
calculations that were not feasible before
Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations
We describe a novel iterative strategy for Kohn-Sham density functional
theory calculations aimed at large systems (> 1000 electrons), applicable to
metals and insulators alike. In lieu of explicit diagonalization of the
Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ
a two-level Chebyshev polynomial filter based complementary subspace strategy
to: 1) compute a set of vectors that span the occupied subspace of the
Hamiltonian; 2) reduce subspace diagonalization to just partially occupied
states; and 3) obtain those states in an efficient, scalable manner via an
inner Chebyshev-filter iteration. By reducing the necessary computation to just
partially occupied states, and obtaining these through an inner Chebyshev
iteration, our approach reduces the cost of large metallic calculations
significantly, while eliminating subspace diagonalization for insulating
systems altogether. We describe the implementation of the method within the
framework of the Discontinuous Galerkin (DG) electronic structure method and
show that this results in a computational scheme that can effectively tackle
bulk and nano systems containing tens of thousands of electrons, with chemical
accuracy, within a few minutes or less of wall clock time per SCF iteration on
large-scale computing platforms. We anticipate that our method will be
instrumental in pushing the envelope of large-scale ab initio molecular
dynamics. As a demonstration of this, we simulate a bulk silicon system
containing 8,000 atoms at finite temperature, and obtain an average SCF step
wall time of 51 seconds on 34,560 processors; thus allowing us to carry out 1.0
ps of ab initio molecular dynamics in approximately 28 hours (of wall time).Comment: Resubmitted version (version 2
Parallelization of the exact diagonalization of the t-t'-Hubbard model
We present a new parallel algorithm for the exact diagonalization of the
-Hubbard model with the Lanczos-method. By invoking a new scheme of
labeling the states we were able to obtain a speedup of up to four on 16 nodes
of an IBM SP2 for the calculation of the ground state energy and an almost
linear speedup for the calculation of the correlation functions. Using this
algorithm we performed an extensive study of the influence of the next-nearest
hopping parameter in the -Hubbard model on ground state energy and
the superconducting correlation functions for both attractive and repulsive
interaction.Comment: 18 Pages, 1 table, 8 figures, Latex uses revtex, submitted to Comp.
Phys. Com
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