Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

The time-dependent two-particle reduced density matrix method: LiH in strong laser fields

Fabian Lackner, Iva Březinová, Takeshi Sato, Kenichi L. Ishikawa, Joachim Burgdörfer

Published Sep 7, 2015• 2 citations
Publisher

Abstract

We present a time-dependent many-body theory that is based on the propagation of the two-particle reduced density matrix (2-RDM) [1]. We apply our method to simulate the non-linear response of one-dimensional lithium hydride in femtosecond mid-IR laser pulses.
DOI
10.1088/1742-6596/635/11/112084

Related papers

Propagating two-particle reduced density matrices without wave functions

Fabian Lackner, Iva Březinová, Takeshi Sato +2 more

Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. In this paper we develop a time-dependent many-body theory that is based on the two-particle reduced density matrix (2-RDM). We present a closed equation of motion for the 2-RDM by developing a reconstruction functional for the three-particle reduced density matrix (3-RDM) that preserves norm, energy, and spin symmetries during time propagation. We show that approximately enforcing $N$-representability during time evolution is essential for achieving stable solutions. As a prototypical test case which features long-range Coulomb interactions we employ the one-dimensional model for lithium hydride (LiH) in strong infrared laser fields. We probe both one-particle observables such as the time-dependent dipole moment and two-particle observables such as the pair density and mean electron-electron interaction energy. Our results are in very good agreement with numerically exact solutions for the $N$-electron wave function obtained from the multiconfigurational time-dependent Hartree-Fock method.

arXiv:1411.0495•Physical Review A•Feb 11, 2015•54 citations

Time-Dependent Quantum Many-Body Systems: Linear Response, Electronic Transport, and Reduced Density Matrices

Heiko Appel

Time-dependent density functional theory (TDDFT) provides a successful approach to calculate excitation energies of atomic and molecular systems. In part I of this work we present a double-pole approximation (DPA) to the response equations of TDDFT. The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single- pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. Several critical pole separations can be identified, e.g. we find that the pole coupling can cause transitions to vanish entirely from the optical spectrum. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange- correlation kernel fxc from experimental input. This can serve as benchmark for the construction of future approximations for the kernel fxc. Reduced density matrix functional theory (RDMFT) has emerged recently as promising candidate to treat strongly correlated electronic many-body systems beyond traditional density functional theory (DFT). The research within RDMFT was so far focussed on the static theory. In this work we attempt some first steps towards a time-dependent generalization of RDMFT. In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schrödinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single- particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schrödinger equation. We consider the propagation of finite mesoscopic systems and demonstrate the limitations of such an approach. To overcome the shortcomings of a description of quantum transport in terms of finite systems we develop a time-propagation scheme for extended states which utilizes a mixed basis representation. Our discretization scheme allows to treat central device and lead regions on the same footing thus preventing artificial reflections at grid boundaries.

•Jan 1, 2007•10 citations

Dynamics of correlations of fermions in lattices : application of the time-dependent two-particle reduced density matrix method

Stefan Donsa

Correlations in many-body quantum states lead to interesting phenomena while at the same time being enormously difficult to describe theoretically. Recent experiments conducted with ultracold atoms in optical lattices allow to explore quantum many-body correlations in a controlled and tunable way. The underlying theoretical model is the single-band Hubbard model. In this thesis we investigate the one-dimensional Hubbard model by applying the newly developed time-dependent two-particle reduced density matrix method. The method is based upon the assumption that three-particle correlations are negligible. We assess this approximation for equilibrium and non-equilibrium states. We show that the method is well suited for weakly interacting and weakly correlated systems.

•Oct 1, 2015•0 citations

Time-Dependent Density Functional Theory for Intense Laser-Matter Interaction

Michael Ruggenthaler

In order to properly describe the dynamics of a many-particle system in strong, time-dependent fields, a nonperturbative treatment of all constituents and of their correlation is needed. An ab initio solution of the time-dependent many-body Schrödinger equation is only feasible for simple systems. Hence, for many-electron systems in intense laser fields practicable methods for solving the quantum-mechanical many-body problem are required. An formally exact approach is the time-dependent density functional theory. In this work a mathematically rigorous formulation of the foundations of this theory is given. Further the non-locality in time of the exchange-correlation functionals is examined, and we formally define the notion of "quantum memory". We investigate the fundamental process of Rabi oscillations from a density-functional point of view and find the few-level approximation to be in conflict with the basis of time-dependent density functional theory. Finally, we apply the theory to calculate the electron dynamics of C60 in intense laser pulses. Although the laser light is far off-resonant with respect to the collective modes of the C60 the multi-electron dynamics strongly influences the harmonic spectra. The efficiency of this multi-particle recollision process with respect to the usual single active electron approximation of high-order harmonic generation is estimated by two analytical models.

•Jan 1, 2009•0 citations

Incorporating decoherence into solid-state time-dependent density functional theory

Isabella Floss, C. Lemell, Kazuhiro Yabana +1 more

Time-dependent density functional theory (TDDFT) has developed into an efficient and versatile description of realistic extended many-electron systems driven, e.g., by strong laser fields. It accounts for the fully coherent evolution of the $N$-electron wave packet representing an isolated system. Decoherence as encountered in open systems by coupling to external degrees of freedom of a bath of, e.g., phonons or defects, is, by construction, absent. In this work we present an open-quantum system (OQS) extension of TDDFT accounting for dephasing and decoherence due to electron-phonon or defect scattering. We test the OQS-TDDFT for high-harmonic generation and irreversible changes of dielectric properties in solids driven by strong ir and mid-ir laser pulses. We present applications to diamond as a prototypical wide band-gap dielectric. For weak pulses we demonstrate the equivalence of OQS-TDDFT with the solution of the Bloch equations for the reduced one-particle density matrix while differences appear at high excitation densities. Our study highlights the importance of the accurate representation of the band structure in simulations of the harmonic spectrum. Narrow avoided crossings within the Brillouin zone can give rise to Bloch-type oscillations.

Physical review. B./Physical review. B•Jun 3, 2019•41 citations

Necessary N-representability Constraints from Time-reversal Symmetry for Periodic Systems

Nicholas C. Rubin, David A. Mazziotti

The variational calculation of the two-electron reduced density matrix (2-RDM) is extended to periodic molecular systems. If the 2-RDM theory is extended to the periodic case without consideration of time-reversal symmetry, however, it can yields energies that are significantly lower than the correct energies. We derive and implement linear constraints that enforce time-reversal symmetry on the 2-RDM without destroying its computationally favorable block-diagonal structure from translational invariance. Time-reversal symmetry is distinct from space-group or spin (SU(2)) symmetries which can be expressed by unitary transformations. The time-reversal symmetry constraints are demonstrated through calculations of the metallic hydrogen chain and the one-dimensional lithium hydride crystal.

arXiv:1606.06262•Jun 20, 2016•1 citation
Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. In this paper we develop a time-dependent many-body theory that is based on the two-particle reduced density matrix (2-RDM). We present a closed equation of motion for the 2-RDM by developing a reconstruction functional for the three-particle reduced density matrix (3-RDM) that preserves norm, energy, and spin symmetries during time propagation. We show that approximately enforcing NNN-representability during time evolution is essential for achieving stable solutions. As a prototypical test case which features long-range Coulomb interactions we employ the one-dimensional model for lithium hydride (LiH) in strong infrared laser fields. We probe both one-particle observables such as the time-dependent dipole moment and two-particle observables such as the pair density and mean electron-electron interaction energy. Our results are in very good agreement with numerically exact solutions for the NNN-electron wave function obtained from the multiconfigurational time-dependent Hartree-Fock method.
Time-dependent density functional theory (TDDFT) provides a successful approach to calculate excitation energies of atomic and molecular systems. In part I of this work we present a double-pole approximation (DPA) to the response equations of TDDFT. The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single- pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. Several critical pole separations can be identified, e.g. we find that the pole coupling can cause transitions to vanish entirely from the optical spectrum. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange- correlation kernel fxc from experimental input. This can serve as benchmark for the construction of future approximations for the kernel fxc. Reduced density matrix functional theory (RDMFT) has emerged recently as promising candidate to treat strongly correlated electronic many-body systems beyond traditional density functional theory (DFT). The research within RDMFT was so far focussed on the static theory. In this work we attempt some first steps towards a time-dependent generalization of RDMFT. In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schrödinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single- particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schrödinger equation. We consider the propagation of finite mesoscopic systems and demonstrate the limitations of such an approach. To overcome the shortcomings of a description of quantum transport in terms of finite systems we develop a time-propagation scheme for extended states which utilizes a mixed basis representation. Our discretization scheme allows to treat central device and lead regions on the same footing thus preventing artificial reflections at grid boundaries.
Correlations in many-body quantum states lead to interesting phenomena while at the same time being enormously difficult to describe theoretically. Recent experiments conducted with ultracold atoms in optical lattices allow to explore quantum many-body correlations in a controlled and tunable way. The underlying theoretical model is the single-band Hubbard model. In this thesis we investigate the one-dimensional Hubbard model by applying the newly developed time-dependent two-particle reduced density matrix method. The method is based upon the assumption that three-particle correlations are negligible. We assess this approximation for equilibrium and non-equilibrium states. We show that the method is well suited for weakly interacting and weakly correlated systems.
In order to properly describe the dynamics of a many-particle system in strong, time-dependent fields, a nonperturbative treatment of all constituents and of their correlation is needed. An ab initio solution of the time-dependent many-body Schrödinger equation is only feasible for simple systems. Hence, for many-electron systems in intense laser fields practicable methods for solving the quantum-mechanical many-body problem are required. An formally exact approach is the time-dependent density functional theory. In this work a mathematically rigorous formulation of the foundations of this theory is given. Further the non-locality in time of the exchange-correlation functionals is examined, and we formally define the notion of "quantum memory". We investigate the fundamental process of Rabi oscillations from a density-functional point of view and find the few-level approximation to be in conflict with the basis of time-dependent density functional theory. Finally, we apply the theory to calculate the electron dynamics of C60 in intense laser pulses. Although the laser light is far off-resonant with respect to the collective modes of the C60 the multi-electron dynamics strongly influences the harmonic spectra. The efficiency of this multi-particle recollision process with respect to the usual single active electron approximation of high-order harmonic generation is estimated by two analytical models.
Time-dependent density functional theory (TDDFT) has developed into an efficient and versatile description of realistic extended many-electron systems driven, e.g., by strong laser fields. It accounts for the fully coherent evolution of the NNN-electron wave packet representing an isolated system. Decoherence as encountered in open systems by coupling to external degrees of freedom of a bath of, e.g., phonons or defects, is, by construction, absent. In this work we present an open-quantum system (OQS) extension of TDDFT accounting for dephasing and decoherence due to electron-phonon or defect scattering. We test the OQS-TDDFT for high-harmonic generation and irreversible changes of dielectric properties in solids driven by strong ir and mid-ir laser pulses. We present applications to diamond as a prototypical wide band-gap dielectric. For weak pulses we demonstrate the equivalence of OQS-TDDFT with the solution of the Bloch equations for the reduced one-particle density matrix while differences appear at high excitation densities. Our study highlights the importance of the accurate representation of the band structure in simulations of the harmonic spectrum. Narrow avoided crossings within the Brillouin zone can give rise to Bloch-type oscillations.
The variational calculation of the two-electron reduced density matrix (2-RDM) is extended to periodic molecular systems. If the 2-RDM theory is extended to the periodic case without consideration of time-reversal symmetry, however, it can yields energies that are significantly lower than the correct energies. We derive and implement linear constraints that enforce time-reversal symmetry on the 2-RDM without destroying its computationally favorable block-diagonal structure from translational invariance. Time-reversal symmetry is distinct from space-group or spin (SU(2)) symmetries which can be expressed by unitary transformations. The time-reversal symmetry constraints are demonstrated through calculations of the metallic hydrogen chain and the one-dimensional lithium hydride crystal.