Theoretical Quantum Dynamics
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Quantum many-body physics and quantum chemistry


Since the 1920s theoretical physics knows how to solve, in principle, all questions from atomic, molecular, and solid state physics. The key is the many-body Schrödinger equation which, unfortunately, is not possible to solve exactly for all but the smallest systems such as the helium atom even when the largest supercomputers are used. One has to rely on approximations to be able to address any questions of practical interest.

We utilize and develop state of the art quantum many-body theory approximations and apply them to current topics of interest such as ultra-cold atoms, molecule-surface interactions, and color centers in alkali-halide crystals.



Hierarchy of many-body theories

Density functional theory has become the workhorse of electronic structure theory. However, the introduction of orbitals by the Kohn-Sham ansatz scales cubically with system size, making the treatment of large structures numerically unfeasible. Orbital-free density functional theory scales linearly with system size, allowing for the treatment of millions of atoms. However, currently available orbital-free functionals cannot accurately treat heavier atoms, e.g., transition metals. By the introduction of angular-momentum dependent functionals, we greatly increase accuracy without inducing substantial numerical overhead. This research is done in collaboration with Prof. Emily Carter from Princeton.

Selected publications:
Angular-Momentum-Dependent Orbital-Free Density Functional Theory
Y. Ke, F. Libisch, J. Xia, L.-W. Wang, and E. A. Carter  Physical Review Letters 111, 066402 (2013)

Angular momentum dependent orbital-free density functional theory: Formulation and implementation
Y. Ke, F. Libisch, J. Xia, and E. A. Carter  Physical Review B 89, 155112 (2014)

Embedding: combining different quantum many-body methods

Solving the quantum mechanical many-particle Schrödinger equation is numerically quite challenging: exact solutions are feasible only for two-particle systems. Several levels of approximation have been devised, from highly accurate (and numerically very demanding) quantum chemistry correlated wavefunction methods, Kohn-Sham density functional theory, to empirical tight-binding methods. For more complex systems, one is usually constrained to the most accurate method that can still treat the required system size. However, many problems are difficult to tackle with a single method. Consider, for example, the interaction between a metal surface and approaching oxygen molecules, as of interest for many catalytic processes: while density functional theory handles the extended metal surface well, accurate treatment of the charge transfer processes from the surface to the oxygen molecule requires expensive correlated wavefunction methods. This research is done in collaboration with Prof. Emily Carter from Princeton.

Selected publications:
Origin of the Energy Barrier to Chemical Reactions of O2 on Al(111): Evidence for Charge Transfer, Not Spin Selection
F. Libisch, C. Huang, P. Liao, M. Pavone, and E. A. Carter  Physical Review Letters 109, 198303 (2012)

Embedded Correlated Wavefunction Schemes: Theory and Application
F. Libisch, C. Huang, and E. A. Carter  Accounts of Chemical Research, 47, 2768 (2014)

The two-particle reduced density matrix of the ground state of a one-dimensional LiH model

The time-dependent two-particle reduced density matrix method

We are developing a new approach for the theoretical description of correlated many-body quantum dynamics and test it on systems containing several quantum particles. The theoretical description of correlated quantum many-body systems is one of the major challenges in nowadays theoretical physics. Quantum correlations between particles occur at practically all levels of complexity: from multi-photon ionization of atoms to high temperature superconductivity in solids. While (time-dependent) density functional theory has been a major step forward, the form of the energy functional is unknown and leaves an ambiguity which can be fixed only for specific problems. The fundamental object in our theory is the two-particle reduced density matrix which measures the distribution of pairs and thus fully accounts for correlations at the two-particle level. This work is an extension of the time-independent two-particle density matrix method which has been developed by other groups and has been successfully tested for molecules. As a testing ground we use ultracold atomic systems of several atoms trapped in optical lattices and strong-field ionization of small molecules. This research is carried out in collaboration with the group of Prof. Kenichi Ishikawa from Tokyo.

Selected publications:
Propagating two-particle reduced density matrices without wave functions
Fabian Lackner, Iva Brezinova et al. Phys. Rev. A 91, 023412 (2015)

High-harmonic spectra from time-dependent two-particle reduced-density-matrix theory
Fabian Lackner, Iva Brezinova et al. Phys. Rev. A 95, 033414 (2017)

Hartree-Fock orbital of the F-center in an embedded lithium-fluoride cluster

Color centers in alkali-halide crystals

We investigate the absorption mechanisms of F-type color centers in alkali-halide crystals applying high-level Quantum Chemistry methods. An F-type color center consists of a single electron trapped in an anionic vacancy. Their absorption energies show an interesting scaling behaviour as a function of the crystal lattice constant known as the Mollwo--Ivey relation. Within the framework of the embedded cluster approach we investigate the formation of the electron confinement and disentangle its contributions as wall as their scaling behaviour leading to the Mollow--Ivey relation. Another focus is the comparison of two complementary approaches, Quantum Chemistry within finite, embedded clusters and post-DFT methods in periodic supercell calculations. The latter are performed in collaboration with the group of Prof. Peter Blaha of the Vienna University of Technology.

Selected publication:
Ab initio perspective on the Mollwo-Ivey relation for F centers in alkali halides
Paul Tiwald et al. Phys. Rev. B92, 144107 (2015)

F center in lithium fluoride revisited: Comparison of solid-state physics and quantum-chemistry approaches
Ferenc Karsai, Paul Tiwald et al. Phys. Rev. B 89, 125429 (2014)

An initially trapped BEC is expanding in an optical lattice

Bose-Einstein condensates

We investigate transport and expansion of Bose-Einstein condensates (BECs) in potential landscapes such as optical lattices and speckle disorder. Especially in disorder, long standing questions such as the effect of interactions on Anderson localization which leads to exponentially suppressed transport can be addressed. The working horse to describe the dynamics of BECs is the Gross-Pitaevskii equation which is considered to be valid whenever interactions can be considered weak and the depletion of the condensate state is very low. We have found that the Gross-Pitaevskii equation predicts chaotic wavefunctions for the above systems. This, at first sight, mathematical peculiarity has a deep physical meaning. Comparing with the multi-configurational time-dependent Hartree for bosons method which includes true many-body effects we have found that the BEC is strongly depleted or even destroyed. Wave chaos thus hints at heating of the BEC during expansion. This work is done in collaboration with the group of Prof. Cederbaum from Heidelberg and Prof. Alon from Haifa.

Selected publications:
Wave chaos as signature for depletion of a Bose-Einstein condensate
Iva Brezinova et al. Phys. Rev. A 86, 013630 (2012)

Long-time expansion of a Bose-Einstein condensate: Observability of Anderson localization
Stefan Donsa, Harald Hofstätter, Othmar Koch, Joachim Burgdörfer, and Iva Březinová  Phys. Rev. A 96, 043630 (2017)