DFG-RSF: Dynamics of strongly non-equilibrium correlated systems at all time scales: dual representation of functional integral

• Applicants: Professor Dr. Martin Eckstein; Professor Dr. Alexander Lichtenstein
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2016 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 310335100

• Final Report Year: 2022

Final Report Abstract

The aim of the DFG-RSF proposal was to develop the theoretical framework to describe dynamics on very different timescales. This is in particular important for the understanding of the femtosecond and picosecond laser-induced dynamics in correlated solids, in particular in the vicinity of photo-induced phase transitions where relaxation timescale of the order parameter fluctuations and of the electrons can be vastly different. A proper description of the dynamics in this case must capture the coupling of bosonic charge, spin, and superconducting fluctuations to the electrons on timescales much longer than the intrinsic electronic timescale. A promising approach to reach this goal is the dual representation of the path integral. In order to establish this formalism, one first needs to overcome two main conceptual and technical challenges: (i) A real-time formulation of diagrammatic equations involving coupled electronic propagators and bosonic susceptibilities, and (ii) a numerical solution for a quantum impurity problem in real time. Within the project, we could make progress in both directions: We developed an impurity solver for dynamical mean field theory which could eventually also be used for real time problems, and we set up a real-time implementation of the FLEX approximation, which includes the coupling of momentum-dependent electronic self-energies and the superconducting order parameter. To make progress from here, it turned out that one of the main numerical challenges are related to the two-time Green’s function formalism, which implies a cubic (quadratic) increase of the computational cost (required memory) with the simulation time. To overcome this bottleneck, we developed a formalism based on a systematic truncation of the memory integrals in nonequilibrium Green’s function simulations, which eventually allowed us to extend the simulations to up to two orders longer in time. This formalism is now used is further ongoing projects, and will be implemented into our open source code NESSi for nonequilibrium Green’s function simulations.

Publications

• Exact diagonalization solver for the extended dynamical mean-field theory, Phys. Rev. B 96, 235149 (2017)
  Medvedeva, Sergei Iskakov, Friedrich Krien, Vladimir V. Mazurenko, Alexander I. Lichtenstein
  
• Relaxation and decoherence of qubits encoded in collective states of engineered magnetic structures, Phys. Rev. B 96, 094410 (2017)
  Alexey M. Shakirov, Alexey N. Rubtsov, Alexander I. Lichtenstein, Pedro Ribeiro
  
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory, Rev. Mod. Phys. 90, 025003 (2018)
  G. Rohringer, H. Hafermann, A. Toschi, A. A. Katanin, A. E. Antipov, M. I. Katsnelson, A. I. Lichtenstein, A. N. Rubtsov, K. Held
  
• Noise Correlations in time- and angular-resolved photoemission spectroscopy, Phys. Rev. B 99, 241111 (2019)
  Christopher Stahl, Martin Eckstein
  
• Electronic and fluctuation dynamics following a quench to the superconducting phase, Phys. Rev. B 103, 035116 (2021)
  Christopher Stahl and Martin Eckstein