Dresden 2011 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 9: CE: (General) Theory 1

TT 9.1: Talk

Monday, March 14, 2011, 14:00–14:15, HSZ 201

Non-equilibrium self-energy-functional theory — •Matthias Balzer and Michael Potthoff — I. Institut für Theoretische Physik, Universität Hamburg, Hamburg

Using standard perturbation theory to all orders, the grand potential of a system of strongly correlated electrons can be expressed as a functional of the self-energy such that the physical self-energy is a stationary point. Non-perturbative approximations can be constructed by restricting the domain of the self-energy functional Ω[Σ] to a subspace of trial self-energies spanned by an exactly solvable reference system [1]. This comprises approximations, such as the dynamical mean-field theory (DMFT) and the variational cluster approximation (VCA).

Here we show that this concept can be extended straightforwardly to the non-equilibrium case. Green’s functions and self-energies have to be defined on the three-branch Keldysh-Matsubara contour in the complex time plane [2], and Ω must be reinterpreted accordingly. The resulting variational scheme is extremely general and provides a rederivation of non-equilibrium DMFT [3], for example.

To discuss practical issues relevant for a numerical implementation of a non-equilibrium VCA, we consider in a first step a coupling of Hubbard-type reference systems consisting of two sites only. Different initial states will be considered, e.g. an uncorrelated Neel state or a correlated singlet state, to study the time evolution of spin correlations.
M. Potthoff, Eur. Phys. J. B 32, 429 (2003).
M. Wagner, Phys. Rev. B 44, 6104 (1991).
J. Freericks et al., Phys. Rev. Lett. 97, 266408 (2006).