Archive 2019

Host: Michael Sentef
Green's functions represent one of the most useful tools for the theoretical description of correlated lattice electrons. In particular, the one-particle Green's function contains information about the spectral properties of the system and can be directly compared to (angular resolved) photoemission spectroscopy experiments. However, also two-particle correlations functions provide very interesting insights into the properties of correlated electron systems as they contain crucial information on response functions such as the magnetic susceptibility or the optical conductivity. In my talk, I will present an overview about the physical content as well as the applications of two-particle Green's and vertex functions in frontier condensed matter research. In particular, I will demonstrate how local frequency-dependent vertices can be used to include non-local correlations effects in interacting many-electron systems on top of the local ones of dynamical mean-field theory (DMFT). While these so-called diagrammatic extensions [1] of DMFT have been successfully exploited to describe collective phenomena such as magnetism and superconductivity, their predictive power is still limited by specific inconsistencies between the one- and the two-particle level [2]. In the final part of my talk, I will present possible solutions to these problems [3] which I will address in the framework of my Emmy Noether project at the University of Hamburg. [more]

Correlated driven-dissipative systems

MPSD Seminar
Driven-dissipative systems represent natural platforms to study non-equilibrium phases. In the first part of the talk, I will present some physical results for which both non-equilibrium conditions and interactions are crucial. I will argue that a prototype model of correlated driven-dissipative lattice bosons, relevant for upcoming generation of circuit QED arrays experiments, exhibits a phase transition where a finite frequency mode becomes unstable, as an effect of quantum interactions and non-equilibrium conditions. In the broken-symmetry phase the corresponding macroscopic order parameter becomes non-stationary and oscillates in time without damping, thus breaking continuous time-translational symmetry. To get some more insights on this transition, I studied the spectral properties of Markovian driven-dissipative quantum systems using a Lehmann representation. Focusing on the nonlinear quantum Van der Pol oscillator as a paradigmatic example, I showed that a sign constraint of spectral functions, which is mathematically exact for closed systems, gets relaxed for open systems; it is eventually replaced by an interplay between dissipation and interactions. In the last part of the talk, I will finally discuss a new method to solve quantum impurity models, small interacting quantum systems coupled to a non-Markovian environment, in presence of additional Markovian dissipation. I will derive a Dyson equation for the time-evolution operator of the reduced density matrix and approximate its self-energy resuming only non-crossing diagrams. I will test this approach on a simple problem of a fermionic impurity. [more]
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