Dual-fermion approach to non-equilibrium strongly correlated problems (Q2908597)

Non-equilibrium physics in strongly correlated systems has been one of the important topics of interest during the last years. Experiments in this field suggested the need for new methods -- both analytical and numerical approaches. Apart from the methods DMRG and NRG, where a physical system is approximated by a finite one-dimensional chain, all other theoretical approaches are perturbative: the Hamiltonian of the system is divided in two parts \(\hat{H} = \hat{H}_0 +\hat{H}_{\text{pert}}\); it solves the \(\hat{H}_0\) part exactly and takes the rest perturbatively into account. Historically the first calculations of the transport through a quantum dot were proposed by Landauer. The further development of this kind of theory lead to the Keldysh technique. Another way to proceed is the weak-coupling approach, which starts from the transport through a non-interacting dot and applies Keldysh diagrammatics in terms of the Coulomb interaction.NEWLINENEWLINEIn this work, the authors make an attempt to generalize the dual fermion approach to models not in equilibrium and present an implementation for the experimentally important case of a hopping quench. They use the path integral approach on the Keldysh contour to formulate the theory and to introduce a proper discretization scheme. The simplified version of this method is much less demanding in terms of time and computational complexity but still gives correct results. This paper presents the basic idea of this method. This paper is divided into four sections.NEWLINENEWLINEAfter the Introduction, a detailed description of the proposed method (Section 2), details of the implementation (Section 3) and a short summary (Section 4) are given.