Institut für Theoretische Physik

Institut für Theoretische Physik Webseite

Projekts:

• Strong electronic correlations in solids
• Multi-configuration time-dependent Hartree approach for electron-nuclear correlation in strong laser fields

Eric Jeckelmann

We study the impact of strong electronic correlations in low-dimensional
materials such as the organic conductor TTF-TCNQ and in nanostructures such
as conducting nanowires. These systems have unusual electronic properties
which cannot be explained by effective one-electron theories such as the
Hartree-Fock approximation, the density functional theory or the Fermi
liquid theory.  Their properties are influenced by strong correlations
between electrons caused by the Coulomb interaction.

From a theoretical point of view, strongly-correlated quantum systems are
very interesting but extremely difficult to study as one has to solve
quantum many-body problems to determine their properties. These systems can
be described by generic lattice models, such as the Hubbard model and its
extensions. We investigate these models to understand the electronic
properties of low-dimensional or nanosized systems, in particular to explain
spectroscopy and transport experiments.

Computer simulations play a crucial role in the study of strongly-correlated
quantum many-body systems. We use numerical methods such as the
density-matrix renormalization group (DMRG) and the time-evolving block
decimation (TEBD) as well as diagrammatic-combinatorial algorithms. For
instance, we have calculated the charge and spin Drude weight of the
one-dimensional extended Hubbard model with on-site repulsion U and
nearest-neighbor repulsion V at quarter filling using the DMRG method. We
have found that the charge Drude weight is discontinuous across the
Kosterlitz-Thouless transition between the conducting Tomonaga-Luttinger
liquid and the charge-density-wave insulator, while the spin Drude weight
varies smoothly and remains finite in both phases (see the figure).

Publication and further information:

• T. Shirakawa and E. Jeckelmann,
  "Charge and spin Drude weight of the one-dimensional extended Hubbard model at quarter filling"
  Phys. Rev. B 79, 195121 (2009)
• More information about the DMRG method

Chirag Jhala and Manfred Lein

The field strength of a high-intensity laser pulse can be comparable to or larger than typical atomic or molecular binding forces. This leads to a multitude of effects involving high excitation, ionization, and fragmentation. Among these phenomena, high-harmonic generation has emerged as a particularly important field of research. HHG spectra from molecules provide information about the molecular structure and have been used to construct electron orbitals. The timedependent Schrödinger equation, although efficacious enough to describe all the relevant non-relativistic physics of atoms and molecules in strong laser fields, is too complex and time consuming to solve for all but very simple systems. A classical description of the nuclei or using the Born-Oppenheimer approximation cannot fully explain the complex interplay between the different degrees of freedom in situations where electrons are excited into high-lying bound or continuum states. The standard method of solving the full TDSE uses a representation of the wave function and Hamiltonian in an appropriate product basis. This approach works very well for small systems but the required computational resources grow exponentially with increasing number of degrees of freedom. For an accurate description of molecules in a strong field, both the response of the electrons and also the nuclear degrees of freedom must be taken into account. Ideally, the dynamics of the different degrees of freedom should be treated fully quantum mechanically. Even simple systems such as the H⁺₂ molecular ion pose a challenge to theoretical description when they are subject to intense laser pulses because large grids or basis sets are required to capture the ionization and fragmentation dynamics in the nonperturbative regime of laser-molecule interactions.

As an alternative to the direct solution of the TDSE, approximate methods have been developed that maintain a fully quantum mechanical picture while alleviating the problem of exponentially growing computational requirements. The multi-configuration time-dependent Hartree approach (MCTDH) is applied to study the electron-nuclear correlation in the dynamics of molecules subject to strong external laser fields, using the example of a model hydrogen molecular ion. The ground state of the system is well described by as few as two single particle functions per degree of freedom. A significantly larger but moderate number of configurations is required to predict laser-induced fragmentation probabilities and high-order harmonic generation spectra accurately, showing that the correlation between electronic and nuclear degree of freedom is strongly increased by the presence of the laser field.

Publications:

• C. Jhala and M. Lein, Multiconfiguration time-dependent Hartree approach for electron-nuclear correlation in strong laser fields,
  Phys. Rev. A 81, 063421 (2010).
• C. Jhala, I. Dreißigacker, and M. Lein, Absorbing boundaries in the meanfield approximation,
  Phys. Rev. A 82, 063415 (2010).

Further information:

• Institute für Theoretische Physik
• Theoretical quantum dynamics group