Calculation Of Ground-state Properties Research Articles

First-principles calculations of structural, electronic, optical and thermoelectric properties of doped binary chalcogenides Sn1-xAxSe (A= Au and Ag) for energy applications

The first-principles based DFT calculations were used to investigate the effect of transition metal (TM) doping on structural, electronic, optical and thermoelectric properties of Sn1-xAxSe (A = Au and Ag). The PBE-GGA approximation is used to calculate ground state properties of TM doped SnSe. These compounds show the presence of type-II intermediate band (IB) at Fermi level. A considerable energy bandgap is present between IB and conduction band. Significant contributions from Ag/Au and Se-atom in valence bands of Sn1-xAxSe (A = Au and Ag) are evident from presented DOS spectra. The calculated Fermi surfaces and Seebeck coefficient (S) confirms p-type nature of these semiconductors. From ε2(ω) spectra, it is evident that Sn1-xAxSe (A = Au and Ag) absorbs maximum number of incident photons in infrared (at ∼0.5 eV) and visible (at ∼2.2 eV) regions. The calculated values of n(ω) are 2.27 and 2.58 for Sn1-xAgxSe and Sn1-xAuxSe, respectively. We can confirm that Sn1-xAxSe (A = Au and Ag) are promising candidates for energy applications (especially solar cells) based on their optoelectronic and thermoelectric properties.

Evaluation of the excitation spectra with diffusion Monte Carlo on an auxiliary bosonic ground state.

We aim to improve upon the variational Monte Carlo (VMC) approach for excitations replacing the Jastrow factor by an auxiliary bosonic (AB) ground state and multiplying it by a fermionic component factor. The instantaneous change in imaginary time of an arbitrary excitation in the original interacting fermionic system is obtained by measuring observables via the ground-state distribution of walkers of an AB system that is subject to an auxiliary effective potential. The effective potential is used to (i) drive the AB system's ground-state configuration space toward the configuration space of the excitations of the original fermionic system and (ii) subtract from a diffusion Monte Carlo (DMC) calculation contributions that can be included in conventional approximations, such as mean-field and configuration interaction (CI) methods. In this novel approach, the AB ground state is treated statistically in DMC, whereas the fermionic component of the original system is expanded in a basis. The excitation energies of the fermionic eigenstates are obtained by sampling a fermion-boson coupling term on the AB ground state. We show that this approach can take advantage of and correct for approximate eigenstates obtained via mean-field calculations or truncated interactions. We demonstrate that the AB ground-state factor incorporates the correlations missed by standard Jastrow factors, further reducing basis truncation errors. Relevant parts of the theory have been tested in soluble model systems and exhibit excellent agreement with exact analytical data and CI and VMC approaches. In particular, for limited basis set expansions and sufficient statistics, AB approaches outperform CI and VMC in terms of basis size for the same systems. The implementation of this method in current codes, despite being demanding, will be facilitated by reusing procedures already developed for calculating ground-state properties with DMC and excitations with VMC.

Structural, electronic, mechanical and phonon properties of half-Heusler GaNiSb, InNiSb and InPdSb alloys via first-principles calculations

In this report, the ground state properties of the half-Heusler GaNiSb, InNiSb and InPdSb alloys in the cubic LiAlSi-type structure, are investigated using the Full Potential Linearized Augmented Plane Wave (FP-LAPW) method as implemented in WIEN2k code, based on Density Functional Theory (DFT). The Perdew–Berke–Ernzerhof (PBE) Generalized Gradient Approximation (GGA) is used for exchange–correlation functional. The calculated formation energies and volume-optimization curves of three different structural configurations (Type 1, Type 2 and Type 3) of these alloys reveal that Type 3 configuration is the most favorable (lowest energy structure) structure. According to the Slater–Pauling rule, the studied alloys are non-magnetic in nature in the stable Type 3 configuration. Therefore, the calculation of ground state properties of these alloys are examined in the Type 3 structural configuration and non-magnetic state. The results of electronic structure and density of states reveal that these alloys are metallic in nature. These alloys are dynamically stable as demonstrated by their calculated phonon dispersion spectra. As the three independent elastic constants C11, C12 and C44 satisfy Born–Huang stability condition, these alloys are stable elastically. The studied alloys are ductile in nature, elastically anisotropic and GaNiSb is found to be stiffer than InNiSb and InPdSb by the calculation of mechanical properties. The present work is in good agreement with the previously reported results.

New effective interactions for hypernuclei in a density-dependent relativistic mean field model

New effective $\Lambda N$ interactions are proposed for the density dependent relativistic mean field model. The multidimensionally constrained relativistic mean field model is used to calculate ground state properties of eleven known $\Lambda$ hypernuclei with $A\ge 12$ and the corresponding core nuclei. Based on effective $NN$ interactions DD-ME2 and PKDD, the ratios $R_\sigma$ and $R_\omega$ of scalar and vector coupling constants between $\Lambda N$ and $NN$ interactions are determined by fitting calculated $\Lambda$ separation energies to experimental values. We propose six new effective interactions for $\Lambda$ hypernuclei: DD-ME2-Y1, DD-ME2-Y2, DD-ME2-Y3, PKDD-Y1, PKDD-Y2 and PKDD-Y3 with three ways of grouping and including these eleven hypernuclei in the fitting. It is found that the two ratios $R_\sigma$ and $R_\omega$ are correlated well and there holds a good linear relation between them. The statistical errors of the ratio parameters in these effective interactions are analyzed. These new effective interactions are used to study the equation of state of hypernuclear matter and neutron star properties with hyperons.

Using quantum annealers to calculate ground state properties of molecules.

Quantum annealers are an alternative approach to quantum computing, which make use of the adiabatic theorem to efficiently find the ground state of a physically realizable Hamiltonian. Such devices are currently commercially available and have been successfully applied to several combinatorial and discrete optimization problems. However, the application of quantum annealers to problems in chemistry remains a relatively sparse area of research due to the difficulty in mapping molecular systems to the Ising model Hamiltonian. In this paper, we review two different methods for finding the ground state of molecular Hamiltonians using Ising model-based quantum annealers. In addition, we compare the relative effectiveness of each method by calculating the binding energies, bond lengths, and bond angles of the H3 + and H2O molecules and mapping their potential energy curves. We also assess the resource requirements of each method by determining the number of qubits and computation time required to simulate each molecule using various parameter values. While each of these methods is capable of accurately predicting the ground state properties of small molecules, we find that they are still outperformed by modern classical algorithms and that the scaling of the resource requirements remains a challenge.

Guided Diffusion Monte Carlo: A Method for Studying Molecules and Ions That Display Large Amplitude Vibrational Motions.

Diffusion Monte Carlo provides an effective and efficient approach for calculating ground state properties of molecular systems based on potential energy surfaces. The approach has been shown to require increasingly large ensembles when intra- and intermolecular vibrations are weakly coupled. We recently proposed a guided variant of diffusion Monte Carlo to address these challenges for water clusters [Lee, V. G. M.; McCoy, A. B. J. Phys. Chem. A 2019, 123, 8063-8070]. In the present study, we extend this approach and apply it to more strongly bound molecular ions, specifically CH5+ and H+(H2O)n=1-4. For the protonated water systems, we show that the guided DMC approach that was developed for studies of (H2O)n can be used to describe the OH stretches and HOH bends in the solvating water molecules, as well as the free OH stretches in the hydronium core. For the hydrogen bonded OH stretches in the H3O+ core of H+(H2O)n and the CH stretches in CH5+, we develop adaptive guiding functions based on the instantaneous structure of the ion of interest. Using these guiding functions, we demonstrate that we are able to obtain converged zero-point energies and ground state wave functions using ensemble sizes that are as small as 10% the size that is needed to obtain similar accuracy from unguided calculations.

Calculating ground-state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches

We introduce an efficient and numerically stable technique to make use of a BCS trial wave function in the computation of correlation functions of strongly correlated quantum fermion systems. The technique is applicable to any projection approach involving paths of independent-fermion propagators, for example in mean-field or auxiliary-field quantum Monte Carlo (AFQMC) calculations. Within AFQMC, in the absence of the sign problem, the methodology allows the use of a BCS reference state which can greatly reduce the required imaginary time of projection, and improves Monte Carlo sampling efficiency and statistical accuracy for systems where pairing correlations are important. When the sign problem is present, the approach provides a powerful generalization of the constrained-path AFQMC technique which usually uses Slater determinant trial wave functions. As a demonstration of the capability of the methodology, we present benchmark results for the attractive Hubbard model, both spin-balanced (no sign problem) and with a finite spin polarization (with sign problem).

Universality of many-body two-nucleon momentum distributions: Correlated nucleon spectral function of complex nuclei

Realistic NN interactions and many-body approaches have been used to calculate ground-state properties of nuclei with A=3, 4, 12, 16, 40, with particular emphasis on various kinds of momentum distributions. It is shown that at proper values of the relative (rel) and center-of-mass (c.m.) momenta, the two-nucleon momentum distribution n_A^{N_1N_2} (k_{rel}, K_{c.m.}, \theta) exhibits the property of factorization, namely n_A^{N_1N_2} (k_{rel}, K_{c.m.}, \theta) \simeq n_{rel}(k_{rel}) n_(c.m.)( K{c.m.}). The factorization of the momentum distributions , bearing a universal character, results from a general property of realistic nuclear wave functions, namely their factorization at short inter-nucleon separations. The factorization of the two-nucleon momentum distribution allows one to develop the correlated part of the nucleon spectral function P(k,E) in terms of a convolution integral involving the product of the many-body, parameter-free relative and c.m. momentum distributions of a given nucleus. It is shown that: (i) the obtained spectral function perfectly satisfies the momentum sum rule, i.e. when it is integrated over the removal energy E, it fully reproduces the momentum distributions obtained from realistic many-body wave functions , (ii) in order to saturate the momentum sum rule at high values of the momentum (k \simeq 5 fm^{-1}) the spectral function has to be integrate up to E \simeq 400 MeV. To sum up a realistic, parameter-free many-body Spectral function has been developed such that : i) a phenomenological convolution spectral function developed in the past is fully justified from a many-body point of view , and (ii) the model dependence which might be present in calculations of inclusive electroweak processes could be reduced by the use of the convolution spectral function developed here.

Variational calculations for ground state properties of liquid 3He injected in a carbon nanotube

Liquid 3He injected in a carbon nanotube is of high interests due to different behavior of the liquid helium in the quasi-one-dimensional systems. In this work, a variational approach has been performed to calculate some thermodynamic properties of this quantum system. In order to do so, a single-walled carbon nanotube containing liquid 3He is considered, applying the Lennard-Jones and Stan–Cole potentials for 3He–3He and 3He–C interactions, respectively. Finally the total energy, equation of state and incompressibility of the system have been calculated. Our calculations show the high values for the incompressibility at high densities, especially for high radii.

Fermions in Two Dimensions: Scattering and Many-Body Properties

Ultracold atomic Fermi gases in two-dimensions (2D) are an increasingly popular topic of research. The interaction strength between spin-up and spin-down particles in two-component Fermi gases can be tuned in experiments, allowing for a strongly interacting regime where the gas properties are yet to be fully understood. We have probed this regime for 2D Fermi gases by performing T=0 ab initio diffusion Monte Carlo calculations. The many-body dynamics are largely dependent on the two-body interactions, therefore we start with an in-depth look at scattering theory in 2D. We show the partial-wave expansion and its relation to the scattering length and effective range. Then we discuss our numerical methods for determining these scattering parameters. We close out this discussion by illustrating the details of bound states in 2D. Transitioning to the many-body system, we use variationally optimized wave functions to calculate ground-state properties of the gas over a range of interaction strengths. We show results for the energy per particle and parametrize an equation of state. We then proceed to determine the chemical potential for the strongly interacting gas.

Superheavy Nuclei in the Quark-Meson-Coupling Model

We present a selection of the first results obtained in a comprehensive calculation of ground state properties of even-even superheavy nuclei in the region of 96 < Z < 136 and 118 < N < 320 from the Quark-Meson-Coupling model (QMC). Ground state binding energies, the neutron and proton number dependence of quadrupole deformations and Q$_\alpha$ values are reported for even-even nuclei with 100 < Z < 136 and compared with available experimental data and predictions of macro-microscopic models. Predictions of properties of nuclei, including Q$_\alpha$ values, relevant for planning future experiments are presented.

Hartree–Fock–Bogoliubov calculation of ground state properties of even–even and odd Mo and Ru isotopes

In a previous work (El Bassem and Oulne (2015) [20]), hereafter referred to as paper I, we have investigated the ground-state properties of Nd, Ce and Sm isotopes within Hartree–Fock–Bogoliubov method with SLy5 Skyrme force in which the pairing strength has been generalized with a new proposed formula. However, that formula is more appropriate for the region of Nd. In this work, we have studied the ground-state properties of both even–even and odd Mo and Ru isotopes. For this, we have used Hartree–Fock–Bogoliubov method with SLy4 Skyrme force, and a new formula of the pairing strength which is more accurate for this region of nuclei. The results have been compared with available experimental data, the results of Hartree–Fock–Bogoliubov calculations based on the D1S Gogny effective nucleon–nucleon interaction and predictions of some nuclear models such as Finite Range Droplet Model (FRDM) and Relativistic Mean Field (RMF) theory.

Quasiparticle bands and structural phase transition of iron from Gutzwiller density-functional theory

We use the Gutzwiller Density Functional Theory to calculate ground-state properties and bandstructures of iron in its body-centered-cubic (bcc) and hexagonal-close-packed (hcp) phases. For a Hubbard interaction $U=9\, {\rm eV}$ and Hund's-rule coupling $J=0.54\, {\rm eV}$ we reproduce the lattice parameter, magnetic moment, and bulk modulus of bcc iron. For these parameters, bcc is the ground-state lattice structure at ambient pressure up to a pressure of $p_{\rm c}=41\, {\rm GPa}$ where a transition to the non-magnetic hcp structure is predicted, in qualitative agreement with experiment ($p_{\rm c}^{\rm exp}=10\ldots 15\, {\rm GPa}$). The calculated bandstructure for bcc iron is in good agreement with ARPES measurements. The agreement improves when we perturbatively include the spin-orbit coupling.

Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing

The infinite Projected Entangled Pair States (iPEPS) algorithm [J. Jordan et al, PRL 101, 250602 (2008)] has become a useful tool in the calculation of ground state properties of 2d quantum lattice systems in the thermodynamic limit. Despite its many successful implementations, the method has some limitations in its present formulation which hinder its application to some highly-entangled systems. The purpose of this paper is to unravel some of these issues, in turn enhancing the stability and efficiency of iPEPS methods. For this, we first introduce the fast full update scheme, where effective environment and iPEPS tensors are both simultaneously updated (or evolved) throughout time. As we shall show, this implies two crucial advantages: (i) dramatic computational savings, and (ii) improved overall stability. Besides, we extend the application of the \emph{local gauge fixing}, successfully implemented for finite-size PEPS [M. Lubasch, J. Ignacio Cirac, M.-C. Ba\~{n}uls, PRB 90, 064425 (2014)], to the iPEPS algorithm. We see that the gauge fixing not only further improves the stability of the method, but also accelerates the convergence of the alternating least squares sweeping in the (either "full" or "fast full") tensor update scheme. The improvement in terms of computational cost and stability of the resulting "improved" iPEPS algorithm is benchmarked by studying the ground state properties of the quantum Heisenberg and transverse-field Ising models on an infinite square lattice.

Gutzwiller density functional theory: a formal derivation and application to ferromagnetic nickel

We present a detailed derivation of the Gutzwiller density functional theory (DFT) that covers all conceivable cases of symmetries and Gutzwiller wave functions. The method is used in a study of ferromagnetic nickel where we calculate ground state properties (lattice constant, bulk modulus, spin magnetic moment) and the quasi-particle band structure. Our method resolves most shortcomings of an ordinary density functional calculation on nickel. However, the quality of the results strongly depends on the particular choice of the double-counting correction. This constitutes a serious problem for all methods that attempt to merge DFT with correlated-electron approaches based on Hubbard-type local interactions.

Dynamic response of silicon nanostructures at finite frequency: An orbital-free density functional theory and non-equilibrium Green's function study

Orbital-free density functional theory (OFDFT) replaces the wavefunction in the kinetic energy by an explicit energy functional and thereby speeds up significantly the calculation of ground state properties of the solid state systems. So far, the application of OFDFT has been centered on closed systems and less attention is paid on the transport properties in open systems. In this paper, we use OFDFT and combine it with non-equilibrium Green's function to simulate equilibrium electronic transport properties in silicon nanostructures from first principles. In particular, we study ac transport properties of a silicon atomic junction consisting of a silicon atomic chain and two monoatomic leads. We have calculated the dynamic conductance of this atomic junction as a function of ac frequency with one to four silicon atoms in the central scattering region. Although the system is transmissive with dc conductance around 4 to 5 e2/h, capacitive-like behavior was found in the finite frequency regime. Our analysis shows that, up to 0.1 THz, this behavior can be characterized by a classic RC circuit consisting of two resistors and a capacitor. One resistor gives rise to dc resistance and the other one accounts for the charge relaxation resistance with magnitude around 0.2 h/e2 when the silicon chain contains two atoms. It was found that the capacitance is around 5 aF for the same system.

Hartree–Fock calculation for excited states

AbstractThe Hartree–Fock (HF) method, widely used for the calculation of ground state properties, in recent years has been extended for calculating excited states. In this article, we develop an approach, which does not require time consuming calculations and can give a good approximation for the excitation energies. The method is based on the fact that the subspaces of the occupied and virtual orbitals are mutually orthogonal. We test the accuracy of our method by evaluating the excited state wavefunctions and the corresponding energies for the Li, N, F, Ne, and Na atoms and for the BeH and CH molecules, and we found good agreement with configuration interaction and experimental results. © 2012 Wiley Periodicals, Inc.

Polaronic Properties of an Ion in a Bose-Einstein Condensate in the Strong-Coupling Limit

Cold atoms can be used to model the Frohlich polaron Hamiltonian using an impurity in a condensate. To probe the strong-coupling regime (which remains elusive in the solid state) charged impurities can be better suited that neutral impurities. However, the ion–atom interaction leads to a stronger depletion of the condensate as compared to the depletion from interaction with neutral impurities, and a good correspondence between the Frohlich Hamiltonian and the cold atom system is only possible when the Bogoliubov approximation is valid. We use a strong-coupling variational approach to estimate an upper limit to the ion-atom coupling strength (expressed through a dimensionless coupling constant). The all-coupling path integral approach is used to estimate the values of the coupling constant that would need to be reached to probe the strong-coupling polaron physics. From these two approaches, we identify a regime where ions in condensates can model strong-coupling polarons and we calculate ground state properties in this regime.

Matrix product state approach for a two-lead multilevel Anderson impurity model

We exploit the common mathematical structure of the numerical renormalization group and the density matrix renormalization group, namely, matrix product states, to implement an efficient numerical treatment of a two-lead, multi-level Anderson impurity model. By adopting a star-like geometry, where each species (spin and lead) of conduction electrons is described by its own Wilson chain, instead of using a single Wilson chain for all species together, we achieve a very significant reduction in the numerical resources required to obtain reliable results. We illustrate the power of this approach by calculating ground state properties of a four-level quantum dot coupled to two leads. The success of this proof-of-principle calculation suggests that the star geometry constitutes a promising strategy for future calculations the ground state properties of multi-band, multi-level quantum impurity models. Moreover, we show that it is possible to find an "optimal" chain basis, obtained via a unitary transformation (acting only on the index distinguishing different Wilson chains), in which degrees of freedom on different Wilson chains become effectively decoupled from each other further out on the Wilson chains. This basis turns out to also diagonalize the model's chain-to-chain scattering matrix. We demonstrate this for a spinless two-lead model, presenting DMRG-results for the mutual information between two sites located far apart on different Wilson chains, and NRG results with respect to the scattering matrix.

Ground-state properties of the Holstein model near the adiabatic limit

We adapt a variational procedure to calculate ground-state properties of the Holstein model in the adiabatic limit. At strong coupling, this adaption leads to rapid convergence of results. The intermediate coupling regime is further handled with an adaptive algorithm. We also use semiclassically derived results for the adiabatic end point, along with weak coupling perturbation theory. These establish weak and strong coupling (or large and small polaron, respectively) regimes in two dimensions or higher. As is well known, these are connected smoothly, but the crossover becomes increasingly abrupt as the phonon frequency decreases.