Density Matrix Perturbation Research Articles

Tailoring the terahertz absorption in the quantum wells

In this paper the optical properties of an inverse parabolic quantum well mixed with a square quantum well has been investigated. The Schrödinger equation has been solved using the numerical method and all the eigen-energies and wave functions are obtained. Furthermore, using the density matrix approach and perturbation method, the absorption coefficients and refractive index changes have been calculated and analyzed. The results show that for appropriate values of quantum well parameters the absorption coefficient peak lies in the terahertz frequency range. Also, the stability of the absorption peak due to small random defects in quantum well is investigated.

Canonical density matrix perturbation theory.

Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free-energy ensembles in tight-binding, Hartree-Fock, or Kohn-Sham density-functional theory. The canonical density matrix perturbation theory can be used to calculate temperature-dependent response properties from the coupled perturbed self-consistent field equations as in density-functional perturbation theory. The method is well suited to take advantage of sparse matrix algebra to achieve linear scaling complexity in the computational cost as a function of system size for sufficiently large nonmetallic materials and metals at high temperatures.

Strictly single-site DMRG algorithm with subspace expansion

We introduce a strictly single-site DMRG algorithm based on the subspace expansion of the Alternating Minimal Energy (AMEn) method. The proposed new MPS basis enrichment method is sufficient to avoid local minima during the optimisation, similarly to the density matrix perturbation method, but computationally cheaper. Each application of $\hat H$ to $|\Psi\rangle$ in the central eigensolver is reduced in cost for a speed-up of $\approx (d + 1)/2$, with $d$ the physical site dimension. Further speed-ups result from cheaper auxiliary calculations and an often greatly improved convergence behaviour. Runtime to convergence improves by up to a factor of 2.5 on the Fermi-Hubbard model compared to the previous single-site method and by up to a factor of 3.9 compared to two-site DMRG. The method is compatible with real-space parallelisation and non-abelian symmetries.

Role of incoherent pumping field on absorption–dispersion properties of probe pulse in a graphene nanostructure under external magnetic field

The optical properties of weak probe light based on quantum coherence and interference in Landau-quantized graphene nanostructure driven by two coherent fields and incoherent pumping field is investigated. The linear dynamical properties of the graphene by means of density matrix method and perturbation theory are discussed. It is found that under certain condition and for appropriate choosing the parameters of the medium, the absorption, dispersion, group index of the weak probe light can be controlled. Moreover, it is shown that by means of incoherent pumping field the superluminal light propagation in the system is accompanied by amplification to make sure that the probe field is amplified as it passes through the system. Moreover, it is observed that the probe amplification can be obtained in the presence or absence of population inversion by properly choosing of system’s parameters. We hope that these results may have useful in the future quantum communicational system and networks.

HONPAS: A linear scaling open‐source solution for large system simulations

HONPAS is an ab initio electronic structure program for linear scaling or O(N) first‐principles calculations of large and complex systems using standard norm‐conserving pseudopotentials, numerical atomic orbitals (NAOs) basis sets, and periodic boundary conditions. HONPAS is developed in the framework of the SIESTA methodology and focuses on the development and implementation of efficient O(N) algorithms for ab initio electronic structure calculations. The Heyd–Scuseria–Ernzerhof (HSE) screened hybrid density functional has been implemented using a NAO2GTO scheme to evaluate the electron repulsion integrals (ERIs) with NAOs. ERI screening techniques allow the HSE functional calculations to be very efficient and scale linearly. The density matrix purification algorithms have been implemented, and the PSUTC2 and SUTC2 methods have been developed to deal with spin unrestricted systems with or without predetermined spin multiplicity, respectively. After the self‐consistent field (SCF) process, additional O(N) post‐SCF calculations for frontier molecular orbitals and maximally localized Wannier functions are also developed and implemented. Finally, an O(N) method based on the density matrix perturbation theory has been proposed and implemented to treat electric field in solids. This article provides an overall introduction to capabilities of HONPAS and implementation details of different O(N) algorithms. © 2014 Wiley Periodicals, Inc.

Electronic and optical properties of InGaAs/GaAs quantum dots with tunable aspect-ratio

In this paper, a combined approach of finite element method (FEM) and quadratic programming optimization method is proposed to investigate the nonuniform equilibrium composition profile of InGaAs / GaAs quantum dots (QDs) in the framework of Gibbs energy optimization (GEO). The proposed QDs are varied with aspect ratio from 0.3 to 0.5. The wave functions of electron and heavy hole are predicted by using the k ⋅ p method. The changes of wave functions before and after optimization can be observed by using composition optimization. Both the eigenvalues and transition energy change obviously with the increasing aspect ratio. The linear optical absorption coefficients corresponding to the interband ground state transition are obtained via the density matrix approach and perturbation expansion method. The numerical results reveal that the aspect ratio and composition profile play significant roles in determining the electronic and optical properties.

A linear- and sublinear-scaling method for calculating NMR shieldings in atomic orbital-based second-order Møller-Plesset perturbation theory

An atomic-orbital (AO) based formulation for calculating nuclear magnetic resonance chemical shieldings at the second-order Møller-Plesset perturbation theory level is introduced, which provides a basis for reducing the scaling of the computational effort with the molecular size from the fifth power to linear and for a specific nucleus to sublinear. The latter sublinear scaling in the rate-determining steps becomes possible by avoiding global perturbations with respect to the magnetic field and by solving for quantities that involve the local nuclear magnetic spin perturbation instead. For avoiding the calculation of the second-order perturbed density matrix, we extend our AO-based reformulation of the Z-vector method within a density matrix-based scheme. Our pilot implementation illustrates the fast convergence with respect to the required number of Laplace points and the asymptotic scaling behavior in the rate-determining steps.

Quantum lithography with classical light

The concept of performing quantum lithography with classical, instead of entangled, light is of great interest for practical implementation. One recent proposal [Hemmer, Muthukrishnan, Scully, and Zubairy, Phys. Rev. Lett. 96, 163603 (2006)] to accomplish this was based on the use of frequency selective multiphoton transitions in a two-level atom. To analyze this possibility we investigate a four-level system theoretically and show that a high-resolution lithography is possible. We quantitatively identify conditions under which high-contrast lithography can be performed without sacrificing high resolution. The approach is a perturbative density matrix method. This model identifies the tradeoff between resolution and contrast as being due to higher-order terms from intermediate-level Rabi oscillations. We propose using positive and negative one-photon detunings to suppress this effect. Allowing higher Rabi frequencies means that shorter interaction time can be used, and this overcomes the degradation in contrast due to population decay. Finally, we generalize our scheme to $\mathbit{N}$-photon lithography.

Quantum correlations in the two-photon decay of few-electron ions

The photon-photon polarization entanglement in the two-photon decay of metastable ionic states has been analyzed in the framework of the density matrix and second-order perturbation theory. Emphasis is placed especially upon the relativistic and non-dipole effects along the hydrogen- and helium-isoelectronic sequence.

Crossover from strong to weak exciton confinement and third-harmonic generation on one-dimensional quantum dots

We study the effects of exciton confinement on the nonlinear optical susceptibility of one-dimensional quantum dots. We use a direct numerical diagonalization to obtain the eigenenergies and eigenstates of the discretized Hamiltonian representing an electron–hole pair confined by a semiparabolic potential and interacting with each other via a Coulomb potential. Density matrix perturbation theory is used to compute the nonlinear optical susceptibilities due to third-harmonic generation and the corresponding nonlinear corrections to the refractive index and absorption coefficient. These quantities are analyzed as a function of ratio between the confinement length L and the exciton Bohr radius a0. The Coulomb potential degrades the uniformity of the level separation. We show that this effect promotes the emergence of multiple resonance peaks in the third-harmonic generation spectrum. In the weak confinement regime β=L/a0≫1, the third-order susceptibility is shown to decay as 1/β8 due to the prevalence of the hydrogenoid character of the exciton eigenstates.

Solution of the Bethe-Salpeter equation without empty electronic states: Application to the absorption spectra of bulk systems

An approach recently developed to solve the Bethe-Salpeter equation within density matrix perturbation theory is extended to the calculation of optical spectra of periodic systems. This generalization requires numerical integrations within the first Brillouin zone that are efficiently performed by exploiting point group symmetries. The technique is applied to the calculation of the optical spectra of bulk Si, diamond C, and cubic SiC. Numerical convergence and the accuracy of the Tamm-Dancoff approximation are discussed in detail.

Polarization correlations in the two–photon decay of hydrogen–like ions

Polarization properties of the photons emitted in the two–photon decay of hydrogen–like ions are studied within the framework of the density matrix and second-order perturbation theory. In particular, we derive the polarization correlation function that gives the probability of the (two–photon) coincidence measurement performed by polarization–sensitive detectors. Detailed calculations of this function are performed for the 2s 1/2 →1s 1/2 transition in neutral hydrogen as well as Xe53 + and U91 + ions. The obtained results allow us to understand the influence of relativistic and non–dipole effects on the polarization correlations in the bound–bound two–photon transitions in heavy ions.

Ab initio calculations of optical absorption spectra: Solution of the Bethe–Salpeter equation within density matrix perturbation theory

We describe an ab initio approach to compute the optical absorption spectra of molecules and solids, which is suitable for the study of large systems and gives access to spectra within a wide energy range. In this approach, the quantum Liouville equation is solved iteratively within first order perturbation theory, with a Hamiltonian containing a static self-energy operator. This procedure is equivalent to solving the statically screened Bethe-Salpeter equation. Explicit calculations of single particle excited states and inversion of dielectric matrices are avoided using techniques based on density functional perturbation theory. In this way, full absorption spectra may be obtained with a computational workload comparable to ground state Hartree-Fock calculations. We present results for small molecules, for the spectra of a 1 nm Si cluster in a wide energy range (20 eV), and for a dipeptide exhibiting charge transfer excitations.

TDDFT Investigation of Surface-Enhanced Raman Scattering of HCN and CN−on Ag20†

Density functional calculations at the BP86/TZP level of theory are employed to examine the structures, binding energies, and vibrational frequencies of HCN-Ag(20) and CN(-)-Ag(20) complexes. Excited states are calculated using time-dependent density functional theory. A short time approximation for the perturbed density matrix and an empirical damping factor are employed to calculate surface-enhanced Raman scattering (SERS) intensities that account for both chemical and electromagnetic enhancement effects. Chemical effects provide 1-2 orders of magnitude enhancement, whereas electromagnetic effects yield up to 6 orders of magnitude enhancement for CN(-) or 5 for HCN. The structures and SERS enhancement factors suggest that multiple bonding configurations may be observed in experiment.

Electronic and optical properties of GaN/AlN quantum dots with adjacent threading dislocations

We present a theory to simulate a coherent GaN QD with an adjacent pure edge threading dislocation by using a finite element method. The piezoelectric effects and the strain modified band edges are investigated in the framework of multi-band k · p theory to calculate the electron and the heavy hole energy levels. The linear optical absorption coefficients corresponding to the interband ground state transition are obtained via the density matrix approach and perturbation expansion method. The results indicate that the strain distribution of the threading dislocation affects the electronic structure. Moreover, the ground state transition behaviour is also influenced by the position of the adjacent threading dislocation.

Comparison of the Auxiliary Density Perturbation Theory and the Noniterative Approximation to the Coupled Perturbed Kohn−Sham Method: Case Study of the Polarizabilities of Disubstituted Azoarene Molecules

We present a theoretical study of the polarizabilities of free and disubstituted azoarenes employing auxiliary density perturbation theory (ADPT) and the noniterative approximation to the coupled perturbed Kohn-Sham (NIA-CPKS) method. Both methods are noniterative but use different approaches to obtain the perturbed density matrix. NIA-CPKS is different from the conventional CPKS approach in that the perturbed Kohn-Sham matrix is obtained numerically, thereby yielding a single-step solution to CPKS. ADPT is an alternative approach to the analytical CPKS method in the framework of the auxiliary density functional theory. It is shown that the polarizabilities obtained using these two methods are in good agreement with each other. Comparisons are made for disubstituted azoarenes, which give support to the push-pull mechanism. Both methods reproduce the same trend for polarizabilities because of the substitution pattern of the azoarene moiety. Our results are consistent with the standard organic chemistry "activating/deactivating" sequence. We present the polarizabilities of the above molecules calculated with three different exchange-correlation functionals and two different auxiliary function sets. The computational advantages of both methods are also discussed.

One-body potentials including electron interactions, and electron densities in crystals

The electron density ρ(r) in the ground state of a crystal can, in principle, be determined by measuring the x-ray intensities at the Bragg reflections. The work presented here has two aims: (1) To propose a method to determine a fundamental one-body potential V(r) solely from a knowledge of the measured charge density ρ(r). (2) To present new results for corrections to Dirac-Slater exchange theory, solely as functionals of the electron density ρ(r). The methods use the density matrix perturbation theory of March and Murray, recasting this into an approximate form suggested by gradient expansions in the density. Contact is made with the work of Herman and his coworkers, who propose a correction to the Dirac-Slater exchange energy of the form . Our work suggests that a term In ρ is also present, though its magnitude is probably small compared with the term proposed by Herman and coworkers [1].

Photon polarization in the two-photon decay of heavy hydrogen-like ions

We have applied the density matrix and second-order perturbation theory in order to re-analyze the two-photon decay of hydrogen-like ions for the polarization of emitted light. Special attention is paid to the linear polarization of one of the photons, while the spin state of the second photon is supposed to be unobserved. For such an “angle-polarization” correlation of the two photons we investigate the contributions that arise from non electric-dipole terms in the expansion of the electron-photon interaction. Detailed calculations are performed for the 2s1/2 →1s1/2 and 3d5/2 →1s1/2 transitions in neutral hydrogen as well as in hydrogen-like uranium.

Auxiliary density perturbation theory

A new approach, named auxiliary density perturbation theory, for the calculation of second energy derivatives is presented. It is based on auxiliary density functional theory in which the Coulomb and exchange-correlation potentials are expressed by auxiliary function densities. Different to conventional coupled perturbed Kohn-Sham equations the perturbed density matrix is obtained noniteratively by solving an inhomogeneous equation system with the dimension of the auxiliary function set used to expand the auxiliary function density. A prototype implementation for the analytic calculation of molecular polarizabilities is presented. It is shown that the polarizabilities obtained with the newly developed auxiliary density perturbation approach match quantitative with the ones from standard density functional theory if augmented auxiliary function sets are used. The computational advantages of auxiliary density perturbation theory are discussed, too.

Linear scaling density matrix perturbation theory for basis-set-dependent quantum response calculations: An orthogonal formulation

Linear scaling density matrix perturbation theory [A. M. N. Niklasson and M. Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is extended to basis-set-dependent quantum response calculations for a nonorthogonal basis set representation. The generalization is achieved by a perturbation-dependent congruence transform, derived from the factorization of the inverse overlap matrix, which transforms the generalized eigenvalue problem to an orthogonal, standard form. With this orthogonalization transform the basis-set-dependent perturbation in the overlap matrix is included in the orthogonalized Hamiltonian, which is expanded in orders of the perturbation. In this way density matrix perturbation theory developed for an orthogonal representation can be applied also to basis-set-dependent response calculations. The method offers an alternative to the previous solution of the basis-set-dependent response problem, based on a nonorthogonal generalization of the density matrix perturbation theory, where the calculations are performed within a purely nonorthogonal setting [A. M. N. Niklasson et al., J. Chem. Phys. 123, 44107 (2005)].