Tackling time-dependent quantum many-body systems with reduced density matrices

Dr. Iva Brezinova
Assistant Professor
Institute for Theoretical Physics
Vienna University of Technology (TU Wien)

Abstract:

Solving the time-dependent Schrödinger equation sufficiently accurately for strongly non-equilibrium or strongly driven quantum many-body systems remains a great challenge to date. This is particularly true for systems where correlations are important and cannot be treated on any mean-field level. Such systems are at the forefront of current experimental research as progress in the creation and manipulation of ultrafast and strong laser fields gave us a toolbox to both pump and probe quantum systems in a controlled way. Interestingly, the methodological developments to treat such systems theoretically lags behind those achieved for ground state problems. The fact that many new experiments have shown that exotic states of matter can be triggered by fast and strong laser fields and that in most cases inter-particle correlations are essential to understand the underlying physics makes theoretical progress even more urgent. In my talk, I will present our approach to tackle time-dependent driven few- and many-body systems based on the two-particle reduced density matrix. Avoiding the wavefunction altogether allows to circumvent the intractable exponential scaling with particle number but other challenges have to be faced. I will review the essential building blocks of our time-dependent two-particle reduced density matrix method and demonstrate applications ranging from laser driven multi-electron atoms to quench dynamics in the Fermi-Hubbard model.