arXiv subjects

Eran Rabani

Publications and source records attributed to Eran Rabani.

At least 91 records · Page 5Linked to original sources

arXiv2015

Time-dependent Stochastic Bethe-Salpeter Approach

A time-dependent formulation for electron-hole excitations in extended finite systems, based on the Bethe-Salpeter equation (BSE), is developed using a stochastic wave function approach. The time-dependent formulation builds on the connection between time-dependent Hartree-Fock (TDHF) theory and configuration-interaction with single substitution (CIS) method. This results in a time dependent Schrödinger-like equation for the quasiparticle orbital dynamics based on an effective Hamiltonian containing direct Hartree and screened exchange terms, where screening is described within the Random Phase Approximation (RPA). To solve for the optical absorption spectrum, we develop a stochastic formulation in which the quasiparticle orbitals are replaced by stochastic orbitals to evaluate the direct and exchange terms in the Hamiltonian as well as the RPA screening. This leads to an overall quadratic scaling, a significant improvement over the equivalent symplectic eigenvalue representation of the BSE. Application of the time-dependent stochastic BSE (TDsBSE) approach to silicon and CdSe nanocrystals up to size of ~3000 electrons is presented and discussed.

cond-mat.mtrl-sci↗

arXiv2014

Sublinear scaling for time-dependent stochastic density functional theory

A stochastic approach to time-dependent density functional theory (TDDFT) is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (? 16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals (NCs) using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.

physics.chem-ph↗

arXiv2014

Phonon dynamics in correlated quantum systems driven away from equilibrium

A general form of a many-body Hamiltonian is considered, which includes an interacting fermionic sub-system coupled to non-interacting extended fermionic and bosonic systems. We show that the exact dynamics of the extended bosonic system can be derived from the reduced density matrix of the sub-system alone, despite the fact that the latter contains information about the sub-system only. The advantage of the formalism is immediately clear: While the reduced density matrix of the sub-system is readily available, the formalism offers access to observables contained in the full density matrix, which is often difficult to obtain. As an example, we consider an extended Holstein model and study the nonequilibrium dynamics of the, so called, "reaction mode" for different model parameters. The effects of the phonon frequency, the strength of the electron-phonon couplings, and the source-drain bias voltage on the phonon dynamics across the bistability are discussed.

cond-mat.str-el↗

arXiv2014

Embedded fragment stochastic density functional theory

We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.

physics.chem-ph↗

arXiv2014

Breaking the theoretical scaling limit for predicting quasi-particle energies: The stochastic GW approach

We develop a formalism to calculate the quasi-particle energy within the GW many-body perturbation correction to the density functional theory (DFT). The occupied and virtual orbitals of the Kohn-Sham (KS) Hamiltonian are replaced by stochastic orbitals used to evaluate the Green function, the polarization potential, and thereby the GW self-energy. The stochastic GW (sGW) relies on novel theoretical concepts such as stochastic time-dependent Hartree propagation, stochastic matrix compression and spatial/temporal stochastic decoupling techniques. Beyond the theoretical interest, the formalism enables linear scaling GW calculations breaking the theoretical scaling limit for GW as well as circumventing the need for energy cutoff approximations. We illustrate the method for silicon nanocrystals of varying sizes with over 3000 electrons.

cond-mat.mes-hall↗

arXiv2014

Nonequilibrium quantum systems with electron-phonon interactions: Transient dynamics and approach to steady state

The nonequilibrium dynamics of a quantum dot with electron-phonon interactions described by a generalized Holstein model is presented. A combination of methodologies including the reduced density matrix formalism, the multilayer multiconfiguration time-dependent Hartree method, and a time-dependent nonequilibrium Green function approach, is used to explore the transient behavior on multiple timescales as the system approaches steady-state. The dot population dynamics on short to intermediate times is governed by the dot-lead hybridization parameter ($Γ$) and by the typical phonon frequency ($ω_{c}$) and depends on the location of the energy level of the dot relative to the bias window. At longer times, the dynamics show a distinct behavior depending on whether the system is in the adiabatic or non-adiabatic regime, with a quantum dot occupation that may depend on the initial preparation of the phonons degrees of freedom. A "phase" diagram of this localization effect as a function of the polaron shift ($λ$) for various phonon frequencies is derived, suggesting the existence of bistability on experimentally observable timescales.

cond-mat.str-el↗

arXiv2014

A Quasi-Classical Mapping Approach to Vibrationally Coupled Electron Transport in Molecular Junctions

We develop a classical mapping approach suitable to describe vibrationally coupled charge transport in molecular junctions based on the Cartesian mapping for many-electron systems [J. Chem. Phys. 137, 154107 (2012)]. To properly describe vibrational quantum effects in the transport characteristics, we introduce a simple transformation rewriting the Hamiltonian in terms of occupation numbers and use a binning function to facilitate quantization. The approach provides accurate results for the nonequilibrium Holstein model for a range of bias voltages, vibrational frequencies and temperatures. It also captures the hallmarks of vibrational quantum effects apparent in step-like structure in the current-voltage characteristics at low temperatures as well as the phenomenon of Franck-Condon blockade.

cond-mat.str-el↗

arXiv2013

A guided stochastic energy-domain formulation of the second order Møller-Plesset perturbation theory

We develop an alternative formulation in the energy-domain to calculate the second order Møller-Plesset (MP2) perturbation energies. The approach is based on repeatedly choosing four random energies using a non-separable guiding function, filtering four random orbitals at these energies, and averaging the resulting Coulomb matrix elements to obtain a statistical estimate of the MP2 correlation energy. In contrast to our time-domain formulation, the present approach is useful for both quantum chemistry and real-space/plane wave basis sets. The scaling of the MP2 calculation is roughly linear with system size, providing a useful tool to study dispersion energies in large systems. This is demonstrated on a structure of 64 fullerenes within the SZ basis as well as on silicon nanocrystals using real-space grids.

physics.chem-ph↗

arXiv2013

The Electronic Structure of CdSe/CdS Core/Shell Seeded Nanorods: Type-I or Quasi-Type-II?

The electronic structure of CdSe/CdS core/shell seeded nanorods of experimentally relevant size is studied using a combination of molecular dynamics and semiempirical pseudopotential techniques, with the aim to address the transition from type-I to a quasi-type-II band alignment. The hole is found to be localized in the core region regardless of its size. The overlap of the electron density with the core region depends markedly on the size of the CdSe core: For small cores, we observe little overlap, consistent with type-II behavior. For large cores, significant core-overlap of a number of excitonic states can lead to type-I behavior. When electron-hole interactions are taken into account, the core-overlap is further increased. Our calculations indicate that the observed transition from type-II to type-I is largely due to simple volume effects, and not to band alignment.

cond-mat.mtrl-sci↗

arXiv2013

Self-averaging stochastic Kohn-Sham density functional theory

We formulate the Kohn-Sham density functional theory (KS-DFT) as a statistical theory in which the electron density is deter-mined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient to converge the total energy per electron to within a predefined statistical error in order to obtain reliable estimates of the electronic band structure, the forces on nuclei, the density and its moments, etc. The fluctuations in the total energy per electron are guaranteed to decay to zero as the system size increases. This facilitates "self-averaging" which leads to the first ever report of sublinear scaling KS-DFT electronic structure. The approach sidesteps calculation of the density matrix and thus is insensitive to its evasive sparseness, as demonstrated here for silicon nanocrystals. The formalism is not only appealing in terms of its promise to far push the limits of application of KS-DFT, but also represents a cognitive change in the way we think of electronic structure calculations as this stochastic theory seamlessly converges to the thermodynamic limit.

cond-mat.mtrl-sci↗

arXiv2013

Generalized projected dynamics for non-system observables of non-equilibrium quantum impurity models

The reduced dynamics formalism has recently emerged as a powerful tool to study the dynamics of non-equilibrium quantum impurity models in strongly correlated regimes. Examples include the non-equilibrium Anderson impurity model near the Kondo crossover temperature and the non-equilibrium Holstein model, for which the formalism provides an accurate description of the reduced density matrix of the system for a wide range of timescales. In this work, we generalize the formalism to allow for non-system observables such as the current between the impurity and leads. We show that the equation of motion for the reduced observable of interest can be closed with the equation of motion for the reduced density matrix and demonstrate the new formalism for a generic resonant level model.

cond-mat.mes-hall↗

arXiv2013

Multiple steady-states in nonequilibrium quantum systems with electron-phonon interactions

The existence of more than one steady-state in a many-body quantum system driven out-of-equilibrium has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. In this Letter, we combine a reduced density matrix formalism with the multilayer multiconfiguration time-dependent Hartree method to address this problem. This allows to obtain a converged numerical solution of the nonequilibrium dynamics. Considering a generic model for quantum transport through a quantum dot with electron-phonon interaction, we prove that a unique steady-state exists regardless of the initial electronic preparation of the quantum dot consistent with the converged numerical results. However, a bistability can be observed for different initial phonon preparations. The effects of the phonon frequency and strength of the electron-phonon couplings on the relaxation to steady-state and on the emergence of bistability is discussed.

cond-mat.str-el↗

arXiv2012

Steady state conductance in a double quantum dot array: The nonequilibrium equation-of-motion Green function approach

We study steady state transport through a double quantum dot array using the equation-of-motion approach to the nonequilibrium Green functions formalism. This popular technique relies on uncontrolled approximations to obtain a closure for a hierarchy of equations, however its accuracy is questioned. We focus on 4 different closures, 2 of which were previously proposed in the context of the single quantum dot system (Anderson impurity model) and were extended to the double quantum dot array, and develop 2 new closures. Results for the differential conductance are compared to those attained by a master equation approach known to be accurate for weak system-leads couplings and high temperatures. While all 4 closures provide an accurate description of the Coulomb blockade and other transport properties in the single quantum dot case, they differ in the case of the double quantum dot array, where only one of the developed closures provides satisfactory results.This is rationalized by comparing the poles of the Green functions to the exact many-particle energy differences for the isolate system. Our analysis provides means to extend the equation-of-motion technique to more elaborate models of large bridge systems with strong electronic interactions.

cond-mat.str-el↗

arXiv2012

Expeditious Stochastic Calculation of Random-Phase Approximation Energies for Thousands of Electrons in 3 Dimensions

A fast method is developed for calculating the Random-Phase-Approximation (RPA) correlation energy for density functional theory. The correlation energy is given by a trace over a projected RPA response matrix and the trace is taken by a stochastic approach using random perturbation vectors. The method scales, at most, quadratically with the system size but in practice, due to self-averaging, requires less statistical sampling as the system grows and the performance is close to linear scaling. We demonstrate the method by calculating the RPA correlation energy for cadmium selenide and silicon nanocrystals with over 1500 electrons. In contrast to 2nd order Møller-Plesset correlation energies, we find that the RPA correlation energies per electron are largely independent on the nanocrystal size.

physics.chem-ph↗

arXiv2012

Expeditious stochastic approach for MP2 energies in large electronic systems

A fast stochastic method for calculating the 2nd order Møller-Plesset (MP2) correction to the correlation energy of large systems of electrons is presented. The approach is based on reducing the exact summation over occupied and unoccupied states to a time-dependent trace formula amenable to stochastic sampling. We demonstrate the abilities of the method to treat systems of thousands electrons using hydrogen passivated silicon spherical nanocrystals represented on a real space grids, much beyond capabilities of present day MP2 implementations.

physics.chem-ph↗

arXiv2012

Multiexciton generation in IV-VI nanocrystals: The role of carrier effective mass, band mixing, and phonon emission

We study the role of the effective mass, band mixing and phonon emission on multiexciton generation in IV-VI nanocrystals. A 4-band k dot p effective mass model, which allows for an independent variation of these parameters, is adopted to describe the electronic structure of the nanocrystals. Multiexciton generation efficiencies are calculated using a Green's function formalism, providing results that are numerically similar to impact excitation. We find that multiexciton generation efficiencies are maximized when the effective mass of the electron and hole are small and similar. Contact with recent experimental results for multiexciton generation in PbS and PbSe is made.

cond-mat.mtrl-sci↗

arXiv2012

Biexciton generation rates in CdSe nanorods are length independent

We study how shape affects multiexciton generation (MEG) rates in a semiconducting nanocrystal by considering CdSe nanorods with varying diameters and aspect ratios. The calculations employ an atomistic semiempirical pseudopotential model combined with an efficacious stochastic approach applied to systems containing up to 20,000 atoms. The effect of nanorod diameter and aspect ratio on multiexciton generation rates is analyzed in terms of the scaling of the density of trion states and the scaling of the Coulomb couplings. Both show distinct scaling from spherical nanocrystals leading to a surprising result where the multiexciton generation rates are roughly independent of the nanorod aspect ratio

cond-mat.mes-hall↗

arXiv2012

A Cartesian Quasi-classical Model to Nonequilibrium Quantum Transport: The Anderson Impurity Model

We apply the recently proposed quasi-classical approach for a second quantized many-electron Hamiltonian in Cartesian coordinates [J. Chem. Phys. 137, 154107 (2012)] to correlated nonequilibrium quantum transport. The approach provides accurate results for the resonant level model for a wide range of temperatures, bias and gate voltages, correcting for the flaws of our recently proposed mapping using action-angle variables. When electron-electron interactions are included, higher order schemes are required to map the two-electron integrals, leading to semi-quantitative results for the Anderson impurity model. In particular, we show that the current mapping is capable of capturing qualitatively the Coulomb blockade effect.

cond-mat.mes-hall↗