o Wider research context / theoretical framework

The investigation of the dynamics of correlated electron systems out of equilibrium is at the forefront of theoretical condensed matter physics. The list of computational approaches that are applicable to both strong correlations and nonequilibrium is however short. In particular, proper treatment of nonlocal correlations beyond one-dimensional systems is missing. NeqParq is designed to fill this gap by implementing a diagrammatic approach at the two-particle level, the parquet equations method, in nonequilibrium. The advantage of the parquet method is that competing nonlocal fluctuations, such as pairing vs spin fluctuations or charge ordering, can be addressed at the same level of approximation. The numerical complexity of this approach made it impossible to go beyond equilibrium. With the groundbreaking methodological developments in the parquet method in recent years, of which I am one of the main contributors, it will be feasible to extend the parquet equations to nonequilibrium.

o Hypotheses/research questions /objectives

The objectives of the project are: (i) finding an Iterative solution of Keldysh parquet equations for the Anderson impurity and Hubbard models in the real-frequency domain; (ii) calculating real-time dynamics of electronic spectra and optical conductivity with a parquet-based algorithm on a time-discretized contour

o Approach/methods

Two-particle diagrammatic method, parquet equations, formulated on Keldysh contour. Real-frequency formulation will be used for steady states. For general case, real-time evolution will be calculated with time discretization. 

o Level of originality / innovation

Solution of parquet equations for a nonequilibrium lattice problem has not been tried before. When successful it will constitute a substantial methodological development of two-particle diagrammatic approaches and allow for unbiased study of nonlocal correlations and ordering tendencies in systems of correlated electrons out of equilibrium. Even the equilibrium element of the project, namely calculating two-particle vertex functions on the real frequency axis for a lattice model is new.

o Primary researchers involved

Anna Kauch