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Dynamical symmetry between spin and charge excitations studied by a plaquette mean-field approach in two dimensions

The real-time dynamics of local occupation numbers in a Hubbard model on a 6x6 square lattice is studied by means of the non-equilibrium generalization of the cluster-perturbation theory. The cluster approach is adapted to studies of two-dimensional lattice systems by using concepts of multiple-scattering theory and a component decomposition of the non-equilibrium Green's function on the Keldysh-Matsubara contour. We consider "classical" initial states formed as tensor products of states on 2x2-plaquettes and trace the effects of the inter-plaquette hopping in the final-state dynamics. Two different initially excited states are considered on an individual plaquette, a fully polarized staggered spin state (Néel) and a fully polarized charge-density wave (CDW). The final-state dynamics is constrained by a dynamical symmetry, i.e. the time-evolution operator and certain observables are invariant under an anti-unitary transformation composed of time reversal, an asymmetric particle-hole, and a staggered sign transformation. We find an interesting interrelation between this dynamical symmetry and the separation of energy and time scales: In case of a global excitation with all plaquettes excited, the initial Néel and the initial CDW states are linked by the transformation. This prevents an efficient relaxation of the CDW state on the short time scale governing the dynamics of charge degrees of freedom. Contrary, the CDW state is found to relax much faster than the Néel state in case of a local excitation on a single plaquette where the symmetry relation between the two states is broken by the coupling to the environment.