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 $1s$ Slater-type orbital function with a series of $p$ 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 $nH_2$ single chain to the quasiatomic two-chain $2nH$ 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, $n=3\div6$. 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 $U/W$ 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 $H_2$ 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 $H_2$-molecular and $H$-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 $H_2$ 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, $(H_{2})_{n}$ 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 $300$ for the fully parallelized solution.Comment: 14 pages, 10 figures, 1 tabl

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 $R\rightarrow R_c=4.1 a_0$, where $R_c$ is the critical value for metal-insulator transition and $a_0=0.53 \AA$ is the Bohr radius. A critical pressure for metallization of solid atomic hydrogen is estimated and is $\sim 10^2 GPa$.Comment: 9 pages, 12 figures, 1 tabl

Spin-triplet paired phases inside ferromagnet induced by Hund's rule coupling and electronic correlations: Application to UGe2\mathrm{UGe}_2

We discuss a mechanism of real-space spin-triplet pairing, alternative to that due to quantum paramagnon excitations, and demonstrate its applicability to $\mathrm{UGe_2}$. Both the Hund's rule ferromagnetic exchange and inter-electronic correlations contribute to the same extent to the equal-spin pairing, particularly in the regime in which the weak-coupling solution does not provide any. The theoretical results, obtained within the orbitally-degenerate Anderson lattice model, match excellently the observed phase diagram for $\mathrm{UGe_2}$ with the coexistent ferromagnetic (FM1) and superconducting ($A_1$-type) phase. Additionally, weak $A_2$- and $A$-type paired phases appear in very narrow regions near the metamaganetic (FM2 $\rightarrow$ FM1) and FM1 $\rightarrow$ paramagnetic first-order phase-transition borders, respectively. The values of magnetic moments in the FM2 and FM1 states are also reproduced correctly in a semiquantitative manner. The Hund's metal regime is also singled out as appearing near FM1-FM2 boundary

Anderson-Kondo lattice Hamiltonian from the Anderson-Lattice model : a modified Schrieffer-Wolff transformation and the effective exchange interactions

We derive the Anderson-Kondo lattice model by applying canonical perturbation expansion for the Anderson-lattice model in direct space. The transformation is carried out up to the fourth order by a modified Schrieffer-Wolff transformation: we separate the part of hybridization term responsible for the high-energy processes (involving the largest in-the-system intraatomic Coulomb interaction between f electrons) and replace it with the virtual processes in higher orders. The higher-order processes lead to three separate exchange interactions. The obtained Hamiltonian contains both the Kondo (f-c) and the superexchange (f-f) interactions, as well as a residual hybridization responsible for the heavy-quasiparticle formation. This effective Hamiltonian can be used to analyze the magnetic or the paired states, as well their coexistence in heavy-fermion systems. The magnitudes of both the Kondo exchange and the superexchange integrals are estimated as a function of bare hybridization magnitude

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 $H_2$ molecules in the presence of a uniform external force $f$ 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 $f$. 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 $f$ 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

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 ($t$-$J$-$U$) model exhibits some unique features of the Cu-doped apatite $\mathrm{Pb_{10-\mathit{x}}Cu_\mathit{x}(PO_4)_{6}O}$. Namely, the paired state appears only for carrier concentration $0.8 \lesssim x < 1$ and is followed by a close-by phase separation into the superconducting and Mott insulating parts. Furthermore, a moderate amount of the bond disorder ($\Delta t / t \lesssim 20 \%$) does not alter essentially the topology with robust Chern number $C=2$ which diminishes beyond that limit. A room-temperature superconductivity is attainable only for the exchange to hopping ratio $J/|t| \ge 1$ if one takes the bare bandwidth suggested by current DFT calculations. The admixture of $s$-wave pairing component is induced by the disorder. The results have been obtained within statistically consistent variational approximation (SGA)