Density Matrix Perturbation Theory Research Articles

Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation.

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

Computational Protocol to Evaluate Electron-Phonon Interactions Within Density Matrix Perturbation Theory.

We present a computational protocol, based on density matrix perturbation theory, to obtain non-adiabatic, frequency-dependent electron–phonon self-energies for molecules and solids. Our approach enables the evaluation of electron–phonon interaction using hybrid functionals, for spin-polarized systems, and the computational overhead to include dynamical and non-adiabatic terms in the evaluation of electron–phonon self-energies is negligible. We discuss results for molecules, as well as pristine and defective solids.

Polarized induced phase grating in a quantized four-level graphene monolayer system.

We discuss the electromagnetically induced grating (EIG) and electromagnetically induced phase grating (EIPG) in a four-level quantized graphene monolayer system. By using the density matrix technique and perturbation theory, we first obtain the self-Kerr nonlinear susceptibility of the graphene system; afterwards, we study the amplitude and phase modulations of the probe light. We discovered that the EIG and EIPG can be found by controlling the elliptically polarized coupling fields that interact with the monolayer graphene system. Owing to the phase modulation of the transmitted light beam, we recognized that the probe strength can also additionally switch from zeroth-order to high-order diffraction. Moreover, we found that the diffraction performance of the grating may be adjusted through tuning the polarization of the coupling light.

Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network.

Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e., dense matrix-matrix multiplications, in mixed-precision arithmetics, which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree-Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low-precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.

Spatio-temporal properties of pulse propagation in a graphene quantum system

In this paper we have theoretically studied the spatial-temporal evolution of electromagnetic light propagation through a four-level graphene quantum system by using density matrix method and perturbation theory. The four-level graphene quantum medium interacted by an elliptical polarized coupling and a weak probe lights, respectively. We present the analytical solution for solving the Maxwell–Bloch equations for graphene and electromagnetic field in space and time domains. Then, we have analyzed the dynamic control of pulse propagation and optical dual switching in such a laser-driven quantum system. Our theoretical findings show that by adjusting the optical parameters such as elliptical angle i.e. phase difference between right-and-left circularly polarized, one can easily control the absorption spectrum and pulse propagation of the probe light in graphene medium. Our results may have potential applications in designing the new quantum devices for usage in quantum information processing.

Notes on density matrix perturbation theory.

Density matrix perturbation theory (DMPT) is known as a promising alternative to the Rayleigh-Schrödinger perturbation theory, in which the sum-over-states (SOS) is replaced by algorithms with perturbed density matrices as the input variables. In this article, we formulate and discuss three types of DMPT, with two of them based only on density matrices: the approach of Kussmann and Ochsenfeld [J. Chem. Phys. 127, 054103 (2007)] is reformulated via the Sylvester equation and the recursive DMPT of Niklasson and Challacombe [Phys. Rev. Lett. 92, 193001 (2004)] is extended to the hole-particle canonical purification (HPCP) from Truflandier et al. [J. Chem. Phys. 144, 091102 (2016)]. A comparison of the computational performances shows that the aforementioned methods outperform the standard SOS. The HPCP-DMPT demonstrates stable convergence profiles but at a higher computational cost when compared to the original recursive polynomial method.

Orbital magneto-optical response of periodic insulators from first principles

Magneto-optical response, i.e. optical response in the presence of a magnetic field, is commonly used for characterization of materials and in optical communications. However, quantum mechanical description of electric and magnetic fields in crystals is not straightforward as the position operator is ill defined. We present a reformulation of the density matrix perturbation theory for time-dependent electromagnetic fields under periodic boundary conditions, which allows us to treat the orbital magneto-optical response of solids at the ab initio level. The efficiency of the computational scheme proposed is comparable to standard linear-response calculations of absorption spectra and the results of tests for molecules and solids agree with the available experimental data. A clear signature of the valley Zeeman effect is revealed in the continuum magneto-optical spectrum of a single layer of hexagonal boron nitride. The present formalism opens the path towards the study of magneto-optical effects in strongly driven low-dimensional systems.

Double-dark-resonance-enhanced Kerr nonlinearity in a single layer of graphene nanostructure

In this paper, a novel scheme is proposed for the giant enhanced Kerr nonlinearity in a single layer of graphene nanostructure based on quantum optics and nonlinear optical sciences. The linear and the nonlinear susceptibility of the monolayer graphene system are presented in details by using the density matrix method and perturbation theory. After deriving the equations of motion in the steady-state regime, we analytically solve the linear and nonlinear susceptibility of the system. Our numerical results show that the giant enhanced Kerr nonlinearity can be obtained in the double-dark-resonance condition with zero linear and nonlinear absorption. Our results may have potential applications in quantum information science in infrared and terahertz regimes.

Level sequence and splitting identification of closely spaced energy levels by angle-resolved analysis of fluorescence light

The angular distribution and linear polarization of the fluorescence light following the resonant photoexcitation is investigated within the framework of the density matrix and second-order perturbation theory. Emphasis has been placed on "signatures" for determining the level sequence and splitting of intermediate (partially) overlapping resonances, if analyzed as a function of the photon energy of the incident light. Detailed computations within the multiconfiguration Dirac-Fock method have been performed especially for the $1s^{2}2s^{2}2p^{6}3s\;\, J_{i}=1/2 \,+\, \gamma_{1} \:\rightarrow\: (1s^{2}2s2p^{6}3s)_{1}3p_{3/2}\;\, J=1/2, \, 3/2 \:\rightarrow\: 1s^{2}2s^{2}2p^{6}3s\;\, J_{f}=1/2 \,+\, \gamma_{2}$ photoexcitation and subsequent fluorescence emission of atomic sodium. A remarkably strong dependence of the angular distribution and linear polarization of the $\gamma_{2}$ fluorescence emission is found upon the level sequence and splitting of the intermediate $(1s^{2}2s2p^{6}3s)_{1}3p_{3/2}\;\, J=1/2, \, 3/2$ overlapping resonances owing to their finite lifetime (linewidth). We therefore suggest that accurate measurements of the angular distribution and linear polarization might help identify the sequence and small splittings of closely-spaced energy levels, even if they can not be spectroscopically resolved.

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.

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.

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.

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.

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)].