57 research outputs found
Phase diagram of the three-dimensional Hubbard model at half filling
We investigate the phase diagram of the three-dimensional Hubbard model at
half filling using quantum Monte Carlo (QMC) simulations. The antiferromagnetic
Neel temperature T_N is determined from the specific heat maximum in
combination with finite-size scaling of the magnetic structure factor. Our
results interpolate smoothly between the asymptotic solutions for weak and
strong coupling, respectively, in contrast to previous QMC simulations. The
location of the metal-insulator transition in the paramagnetic phase above T_N
is determined using the electronic compressibility as criterion.Comment: 6 pages, 6 figures, to be published in Eur. Phys. J. B (2000
Landau levels in a topological insulator
Two recent experiments successfully observed Landau levels in the tunneling
spectra of the topological insulator Bi2Se3. To mimic the influence of a
scanning tunneling microscope tip on the Landau levels we solve the
two-dimensional Dirac equation in the presence of a localized electrostatic
potential. We find that the STM tip not only shifts the Landau levels, but also
suppresses for a realistic choice of parameters the negative branch of Landau
levels.Comment: 4 page
Density functional theory for a model quantum dot: Beyond the local-density approximation
We study both static and transport properties of model quantum dots,
employing density functional theory as well as (numerically) exact methods. For
the lattice model under consideration the accuracy of the local-density
approximation generally is poor. For weak interaction, however, accurate
results are achieved within the optimized effective potential method, while for
intermediate interaction strengths a method combining the exact diagonalization
of small clusters with density functional theory is very successful. Results
obtained from the latter approach yield very good agreement with density matrix
renormalization group studies, where the full Hamiltonian consisting of the dot
and the attached leads has to be diagonalized. Furthermore we address the
question whether static density functional theory is able to predict the exact
linear conductance through the dot correctly - with, in general, negative
answer.Comment: 8 page
Scaling Behavior in the Stable Marriage Problem
We study the optimization of the stable marriage problem. All individuals
attempt to optimize their own satisfaction, subject to mutually conflicting
constraints. We find that the stable solutions are generally not the globally
best solution, but reasonably close to it. All the stable solutions form a
special sub-set of the meta-stable states, obeying interesting scaling laws.
Both numerical and analytical tools are used to derive our results.Comment: 6 pages, revtex, 3 figures. To appear in J. de Physique I, vol 7, No
12 (December
Low density ferromagnetism in the Hubbard model
A single-band Hubbard model with nearest and next-nearest neighbour hopping
is studied for , 2, 3, using both analytical and numerical techniques. In
one dimension, saturated ferromagnetism is found above a critical value of
for a band structure with two minima and for small and intermediate densities.
This is an extension of a scenario recently proposed by M\"uller--Hartmann. For
three dimensions and non-pathological band structures, it is proven that such a
scenario does not work.Comment: 4 pages, 3 postscript figure
Phase diagram of the one-dimensional half-filled extended Hubbard model
We study the ground state of the one-dimensional half-filled Hubbard model
with on-site (nearest-neighbor) repulsive interaction () and
nearest-neighbor hopping . In order to obtain an accurate phase diagram, we
consider various physical quantities such as the charge gap, spin gap,
Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter using the
density-matrix renormalization group technique. We confirm that the BOW phase
appears in a substantial region between the charge-density-wave (CDW) and
spin-density-wave phases. Each phase boundary is determined by multiple means
and it allows us to do a cross-check to demonstrate the validity of our
estimations. Thus, our results agree quantitatively with the renormalization
group results in the weak-coupling regime (), with the
perturbation results in the strong-coupling regime (), and with
the quantum Monte Carlo results in the intermediate-coupling regime. We also
find that the BOW-CDW transition changes from continuous to first order at the
tricritical point and the BOW
phase vanishes at the critical end point .Comment: 4 pages, 5 figure
Spin polarizations and spin Hall currents in a two-dimensional electron gas with magnetic impurities
We consider a two-dimensional electron gas in the presence of Rashba
spin-orbit coupling, and study the effects of magnetic s-wave impurities and
long-range non-magnetic disorder on the spin-charge dynamics of the system. We
focus on voltage induced spin polarizations and their relation to spin Hall
currents. Our results are obtained using the quasiclassical Green function
technique, and hold in the full range of the disorder parameter .Comment: 5 pages, 2 figures. References added, minor stylistic modification
Efficient implementation of the Gutzwiller variational method
We present a self-consistent numerical approach to solve the Gutzwiller
variational problem for general multi-band models with arbitrary on-site
interaction. The proposed method generalizes and improves the procedure derived
by Deng et al., Phys. Rev. B. 79 075114 (2009), overcoming the restriction to
density-density interaction without increasing the complexity of the
computational algorithm. Our approach drastically reduces the problem of the
high-dimensional Gutzwiller minimization by mapping it to a minimization only
in the variational density matrix, in the spirit of the Levy and Lieb
formulation of DFT. For fixed density the Gutzwiller renormalization matrix is
determined as a fixpoint of a proper functional, whose evaluation only requires
ground-state calculations of matrices defined in the Gutzwiller variational
space. Furthermore, the proposed method is able to account for the symmetries
of the variational function in a controlled way, reducing the number of
variational parameters. After a detailed description of the method we present
calculations for multi-band Hubbard models with full (rotationally invariant)
Hund's rule on-site interaction. Our analysis shows that the numerical
algorithm is very efficient, stable and easy to implement. For these reasons
this method is particularly suitable for first principle studies -- e.g., in
combination with DFT -- of many complex real materials, where the full
intra-atomic interaction is important to obtain correct results.Comment: 19 pages, 7 figure
Variational ground states of the two-dimensional Hubbard model
Recent refinements of analytical and numerical methods have improved our
understanding of the ground-state phase diagram of the two-dimensional (2D)
Hubbard model. Here we focus on variational approaches, but comparisons with
both Quantum Cluster and Gaussian Monte Carlo methods are also made. Our own
ansatz leads to an antiferromagnetic ground state at half filling with a
slightly reduced staggered order parameter (as compared to simple mean-field
theory). Away from half filling, we find d-wave superconductivity, but confined
to densities where the Fermi surface passes through the antiferromagnetic zone
boundary (if hopping between both nearest-neighbour and next-nearest-neighbour
sites is considered). Our results agree surprisingly well with recent numerical
studies using the Quantum Cluster method. An interesting trend is found by
comparing gap parameters (antiferromagnetic or superconducting) obtained with
different variational wave functions. They vary by an order of magnitude and
thus cannot be taken as a characteristic energy scale. In contrast, the order
parameter is much less sensitive to the degree of sophistication of the
variational schemes, at least at and near half filling.Comment: 18 pages, 4 figures, to be published in New J. Phy
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