23 research outputs found
Metallization of atomic solid hydrogen within the extended Hubbard model with renormalized Wannier wave functions
We refer to our recent calculations (Eur. Phys. J. B, \textbf{86}, 252
(2013)) of metallization pressure of the three-dimensional simple-cubic crystal
of atomic hydrogen and study the effect on the crucial results concocting from
approximating the Slater-type orbital function with a series of
Gaussians. As a result, we find the critical metallization pressure $p_C = 102\
GPa$. The latter part is a discussion of the influence of zero-point motion on
the stabilizing pressure. We show that in our model the estimate magnitude of
zero-point motion carries a little effect on the critical metallization
pressure at zero temperature.Comment: 4 pages, 5 figures, 1 tabl
Discontinuous transition of molecular-hydrogen chain to the quasi-atomic state: Exact diagonalization - ab initio approach
We obtain in a direct and rigorous manner a transition from a stable
molecular hydrogen single chain to the quasiatomic two-chain
state. We devise an original method composed of an exact diagonalization in the
Fock space combined with an ab initio adjustment of the single-particle wave
function in the correlated state. In this approach the well-known problem of
double-counting the interparticle interaction does not arise at all. The
transition is strongly discontinuous, and appears even for relatively short
chains possible to tackle, . The signature of the transition as a
function of applied force is a discontinuous change of the equilibrium
intramolecular distance. The corresponding change of the Hubbard ratio
reflects the Mott--Hubbard-transition aspect of the atomization. Universal
feature of the transition relation to the Mott criterion for the
insulator--metal transition is also noted. The role of the electron
correlations is thus shown to be of fundamental significance.Comment: 6 pages, 5 figures, 1 tabl
Metallization of solid molecular hydrogen in two dimensions: Mott-Hubbard-type transition
We analyze the pressure-induced metal-insulator transition in a
two-dimensional vertical stack of molecules in x-y plane, and show that
it represents a striking example of the Mott-Hubbard-type transition. Our
combined exact diagonalization approach, formulated and solved in the second
quantization formalism, includes also simultaneous ab initio readjustment of
the single-particle wave functions, contained in the model microscopic
parameters. The system is studied as a function of applied side force
(generalized pressure), both in the -molecular and -quasiatomic states.
Extended Hubbard model is taken at the start, together with longer-range
electron-electron interactions incorporated into the scheme. The stacked
molecular plane transforms discontinuously into a (quasi)atomic state under the
applied force via a two-step transition: the first between molecular insulating
phases and the second from the molecular to the quasiatomic metallic phase. No
quasiatomic insulating phase occurs. All the transitions are accompanied by an
abrupt changes of the bond length and the intermolecular distance (lattice
parameter), as well as by discontinuous changes of the principal electronic
properties, which are characteristic of the Mott-Hubbard transition here
associated with the jumps of the predetermined equilibrium lattice parameter
and the effective bond length. The phase transition can be interpreted in terms
of the solid hydrogen metallization under pressure exerted by e.g., the
substrate covered with a monomolecular film of the vertically stacked
molecules. Both the Mott and Hubbard criteria at the insulator to metal
transition are discussed
Combined shared and distributed memory ab-initio computations of molecular-hydrogen systems in the correlated state: process pool solution and two-level parallelism
An efficient computational scheme devised for investigations of ground state
properties of the electronically correlated systems is presented. As an
example, chain is considered with the long-range
electron-electron interactions taken into account. The implemented procedure
covers: (i) single-particle Wannier wave-function basis construction in the
correlated state, (ii) microscopic parameters calculation, and (iii) ground
state energy optimization. The optimization loop is based on highly effective
process-pool solution - specific root-workers approach. The hierarchical,
two-level parallelism was applied: both shared (by use of Open
Multi-Processing) and distributed (by use of Message Passing Interface) memory
models were utilized. We discuss in detail the feature that such approach
results in a substantial increase of the calculation speed reaching factor of
for the fully parallelized solution.Comment: 14 pages, 10 figures, 1 tabl
Atomization of correlated molecular-hydrogen chain: A fully microscopic Variational Monte-Carlo solution
We discuss electronic properties and their evolution for the linear chain of
molecules in the presence of a uniform external force acting along
the chain. The system is described by an extended Hubbard model within a fully
microscopic approach. Explicitly, the microscopic parameters describing the
intra- and inter-site Coulomb interactions are determined together with the
hopping integrals by optimizing the system ground state energy and the
single-particle wave functions in the correlated state. The many-body wave
function is taken in the Jastrow form and the Variational Monte-Carlo (VMC)
method is used in combination with an ab initio approach to determine the
energy. Both the effective Bohr radii of the renormalized single-particle wave
functions and the many-body wave function parameters are determined for each
. Hence, the evolution of the system can be analyzed in detail as a function
of the equilibrium intermolecular distance, which in turn is determined for
each value. The transition to the atomic state, including the Peierls
distortion stability, can thus be studied in a systematic manner, particularly
near the threshold of the dissociation of the molecular into atomic chain. The
computational reliability of VMC approach is also estimated
Extended Hubbard model with renormalized Wannier wave functions in the correlated state III: Statistically consistent Gutzwiller approximation and the metallization of atomic solid hydrogen
We extend our previous approach (Eur. Phys. J. B, \textbf{74}, 63(2010)) to
modeling correlated electronic states and the metal-insulator transition by
applying the so-called \emph{statistically consistent Gutzwiller approximation}
(SGA) to carry out self-consistent calculations of the renormalized
single-particle Wannier functions in the correlated state. The transition to
the Mott-Hubbard insulating state at temperature T=0 is of weak first order
even if antiferromagnetism is disregarded. The magnitude of the introduced
self-consistent magnetic correlation field is calculated and shown to lead to a
small magnetic moment in the magnetically uniform state. Realistic value of the
applied magnetic field has a minor influence on the metallic-state
characteristics near the Mott-Hubbard lcalization threshold. The whole analysis
has been carried out for an extended Hubbard model on a simple cubic (SC)
lattice and the evolution of physical properties is analyzed as a function of
the lattice parameter for the renormalized 1s-type Wannier functions. Quantum
critical scaling of the selected physical properties is analyzed as a function
of the lattice constant , where is the critical
value for metal-insulator transition and is the Bohr radius. A
critical pressure for metallization of solid atomic hydrogen is estimated and
is .Comment: 9 pages, 12 figures, 1 tabl
High Temperature Superconductivity with Strong Correlations and Disorder: Possible Relevance to Cu-doped Apatite
We examine the properties of topological strongly correlated superconductor
with bond disorder on triangular lattice and demonstrate that our theoretical
(--) model exhibits some unique features of the Cu-doped apatite
. Namely, the paired state
appears only for carrier concentration and is followed by
a close-by phase separation into the superconducting and Mott insulating parts.
Furthermore, a moderate amount of the bond disorder () does not alter essentially the topology with robust Chern number
which diminishes beyond that limit. A room-temperature superconductivity is
attainable only for the exchange to hopping ratio if one takes
the bare bandwidth suggested by current DFT calculations. The admixture of
-wave pairing component is induced by the disorder. The results have been
obtained within statistically consistent variational approximation (SGA)
and molecules with an ab initio optimization of wave functions in correlated state: Electron-proton couplings and intermolecular microscopic parameters
The hydrogen molecules and are analyzed with electronic
correlations taken into account between the electrons exactly. The optimal
single-particle Slater orbitals are evaluated in the correlated state of
by combining their variational determination with the diagonalization of the
full Hamiltonian in the second-quantization language. All electron--ion
coupling constants are determined explicitly and their relative importance is
discussed. Sizable zero-point motion amplitude and the corresponding energy are
then evaluated by taking into account the anharmonic contributions up to the
ninth order in the relative displacement of the ions from their static
equilibrium value. The applicability of the model to the solid molecular
hydrogen is briefly analyzed by calculating intermolecular microscopic
parameters for rectangular configurations.Comment: 14 pages, 14 figures, 6 table
Dot-ring nanostructure: rigorous analysis of many-electron effects
We discuss the quantum dot-ring nanostructure (DRN) as canonical example of a nanosystem, for which the interelectronic interactions can be evaluated exactly. The system has been selected due to its tunability, i.e., its electron wave functions can be modified much easier than in, e.g., quantum dots. We determine many-particle states for Ne = 2 and 3 electrons and calculate the 3- and 4-state interaction parameters, and discuss their importance. For that purpose, we combine the first- and second-quantization schemes and hence are able to single out the component single-particle contributions to the resultant many-particle state. The method provides both the ground- and the first-excited-state energies, as the exact diagonalization of the many-particle Hamiltonian is carried out. DRN provides one of the few examples for which one can determine theoretically all interaction microscopic parameters to a high accuracy. Thus the evolution of the single-particle vs. many-particle contributions to each state and its energy can be determined and tested with the increasing system size. In this manner, we contribute to the wave-function engineering with the interactions included for those few-electron systems