Doublon-holon pair creation in Mott-Hubbard systems in analogy to QED

Via the hierarchy of correlations, we study doublon-holon pair creation in the Mott state of the Fermi-Hubbard model induced by a time-dependent electric field. Special emphasis is placed on the analogy to electron-positron pair creation from the vacuum in quantum electrodynamics (QED). We find that the accuracy of this analogy depends on the spin structure of the Mott background. For Ising type anti-ferromagnetic order, we derive an effective Dirac equation. A Mott state without any spin order, on the other hand, does not explicitly display such a quasi-relativistic behavior.