Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first, and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality, and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation.Comment: 11 page

Range-separated density-functional theory with random phase approximation: detailed formalism and illustrative applications

Using Green-function many-body theory, we present the details of a formally exact adiabatic-connection fluctuation-dissipation density-functional theory based on range separation, which was sketched in Toulouse, Gerber, Jansen, Savin and Angyan, Phys. Rev. Lett. 102, 096404 (2009). Range-separated density-functional theory approaches combining short-range density functional approximations with long-range random phase approximations (RPA) are then obtained as well-identified approximations on the long-range Green-function self-energy. Range-separated RPA-type schemes with or without long-range Hartree-Fock exchange response kernel are assessed on rare-gas and alkaline-earth dimers, and compared to range-separated second-order perturbation theory and range-separated coupled-cluster theory.Comment: 15 pages, 3 figures, 2 table

Quasiparticle band structure of infinite hydrogen fluoride and hydrogen chloride chains

We study the quasiparticle band structure of isolated, infinite HF and HCl bent (zigzag) chains and examine the effect of the crystal field on the energy levels of the constituent monomers. The chains are one of the simplest but realistic models of the corresponding three-dimensional crystalline solids. To describe the isolated monomers and the chains, we set out from the Hartree-Fock approximation, harnessing the advanced Green's function methods "local molecular orbital algebraic diagrammatic construction" (ADC) scheme and "local crystal orbital ADC" (CO-ADC) in a strict second order approximation, ADC(2,2) and CO-ADC(2,2), respectively, to account for electron correlations. The configuration space of the periodic correlation calculations is found to converge rapidly only requiring nearest-neighbor contributions to be regarded. Although electron correlations cause a pronounced shift of the quasiparticle band structure of the chains with respect to the Hartree-Fock result, the bandwidth essentially remains unaltered in contrast to, e.g., covalently bound compounds.Comment: 11 pages, 6 figures, 6 tables, RevTeX4, corrected typoe

Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

A non-linear conjugate gradient optimization scheme is used to obtain excitation energies within the Random Phase Approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size, N, is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular- orbital-free algorithm is found to be robust and computationally efficient providing a first step toward a large-scale, reduced complexity calculation of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent Density Functional theory.Comment: 9 pages, 7 figure

Full configuration interaction approach to the few-electron problem in artificial atoms

We present a new high-performance configuration interaction code optimally designed for the calculation of the lowest energy eigenstates of a few electrons in semiconductor quantum dots (also called artificial atoms) in the strong interaction regime. The implementation relies on a single-particle representation, but it is independent of the choice of the single-particle basis and, therefore, of the details of the device and configuration of external fields. Assuming no truncation of the Fock space of Slater determinants generated from the chosen single-particle basis, the code may tackle regimes where Coulomb interaction very effectively mixes many determinants. Typical strongly correlated systems lead to very large diagonalization problems; in our implementation, the secular equation is reduced to its minimal rank by exploiting the symmetry of the effective-mass interacting Hamiltonian, including square total spin. The resulting Hamiltonian is diagonalized via parallel implementation of the Lanczos algorithm. The code gives access to both wave functions and energies of first excited states. Excellent code scalability in a parallel environment is demonstrated; accuracy is tested for the case of up to eight electrons confined in a two-dimensional harmonic trap as the density is progressively diluted and correlation becomes dominant. Comparison with previous Quantum Monte Carlo simulations in the Wigner regime demonstrates power and flexibility of the method.Comment: RevTeX 4.0, 18 pages, 6 tables, 9 postscript b/w figures. Final version with new material. Section 6 on the excitation spectrum has been added. Some material has been moved to two appendices, which appear in the EPAPS web depository in the published versio

High-dimensional fractionalization and spinon deconfinement in pyrochlore antiferromagnets

The ground states of Klein type spin models on the pyrochlore and checkerboard lattice are spanned by the set of singlet dimer coverings, and thus possess an extensive ground--state degeneracy. Among the many exotic consequences is the presence of deconfined fractional excitations (spinons) which propagate through the entire system. While a realistic electronic model on the pyrochlore lattice is close to the Klein point, this point is in fact inherently unstable because any perturbation $\epsilon$ restores spinon confinement at $T = 0$. We demonstrate that deconfinement is recovered in the finite--temperature region $\epsilon \ll T \ll J$, where the deconfined phase can be characterized as a dilute Coulomb gas of thermally excited spinons. We investigate the zero--temperature phase diagram away from the Klein point by means of a variational approach based on the singlet dimer coverings of the pyrochlore lattices and taking into account their non--orthogonality. We find that in these systems, nearest neighbor exchange interactions do not lead to Rokhsar-Kivelson type processes.Comment: 19 page

First Order Static Excitation Potential: Scheme for Excitation Energies and Transition Moments

We present an approximation scheme for the calculation of the principal excitation energies and transition moments of finite many-body systems. The scheme is derived from a first order approximation to the self energy of a recently proposed extended particle-hole Green's function. A hermitian eigenvalue problem is encountered of the same size as the well-known Random Phase Approximation (RPA). We find that it yields a size consistent description of the excitation properties and removes an inconsistent treatment of the ground state correlation by the RPA. By presenting a hermitian eigenvalue problem the new scheme avoids the instabilities of the RPA and should be well suited for large scale numerical calculations. These and additional properties of the new approximation scheme are illuminated by a very simple exactly solvable model.Comment: 15 pages revtex, 1 eps figure included, corrections in Eq. (A1) and Sec. II

Electron attachment to valence-excited CO

The possibility of electron attachment to the valence $^{3}\Pi$ state of CO is examined using an {\it ab initio} bound-state multireference configuration interaction approach. The resulting resonance has $^{4}\Sigma^{-}$ symmetry; the higher vibrational levels of this resonance state coincide with, or are nearly coincident with, levels of the parent $a^{3}\Pi$ state. Collisional relaxation to the lowest vibrational levels in hot plasma situations might yield the possibility of a long-lived CO$^-$ state.Comment: Revtex file + postscript file for one figur

Ab initio Green's function formalism for band structures

Using the Green's function formalism, an ab initio theory for band structures of crystals is derived starting from the Hartree-Fock approximation. It is based on the algebraic diagrammatic construction scheme for the self-energy which is formulated for crystal orbitals (CO-ADC). In this approach, the poles of the Green's function are determined by solving a suitable Hermitian eigenvalue problem. The method is not only applicable to the outer valence and conduction bands, it is also stable for inner valence bands where strong electron correlations are effective. The key to the proposed scheme is to evaluate the self-energy in terms of Wannier orbitals before transforming it to a crystal momentum representation. Exploiting the fact that electron correlations are mainly local, one can truncate the lattice summations by an appropriate configuration selection scheme. This yields a flat configuration space; i.e., its size scales only linearly with the number of atoms per unit cell for large systems and, under certain conditions, the computational effort to determine band structures also scales linearly. As a first application of the new formalism, a lithium fluoride crystal has been chosen. A minimal basis set description is studied, and a satisfactory agreement with previous theoretical and experimental results for the fundamental band gap and the width of the F 2p valence band complex is obtained.Comment: 20 pages, 3 figures, 1 table, RevTeX4, new section on lithium fluorid

Hilbert space structure of a solid state quantum computer: two-electron states of a double quantum dot artificial molecule

We study theoretically a double quantum dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer with the electron spins in the dots serving as qubits. Such a two-dot system provides the necessary two-qubit entanglement required for quantum computation. We determine the excitation spectrum of two horizontally coupled quantum dots with two confined electrons, and study its dependence on an external magnetic field. In particular, we focus on the splitting of the lowest singlet and triplet states, the double occupation probability of the lowest states, and the relative energy scales of these states. We point out that at zero magnetic field it is difficult to have both a vanishing double occupation probability for a small error rate and a sizable exchange coupling for fast gating. On the other hand, finite magnetic fields may provide finite exchange coupling for quantum computer operations with small errors. We critically discuss the applicability of the envelope function approach in the current scheme and also the merits of various quantum chemical approaches in dealing with few-electron problems in quantum dots, such as the Hartree-Fock self-consistent field method, the molecular orbital method, the Heisenberg model, and the Hubbard model. We also discuss a number of relevant issues in quantum dot quantum computing in the context of our calculations, such as the required design tolerance, spin decoherence, adiabatic transitions, magnetic field control, and error correction.Comment: 22 2-column pages, 11 figures. Published versio