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We express the recently introduced real-time diagrammatic Quantum MonteCarlo, Phys. Rev. B 91, 245154 (2015), in the Larkin-Ovchinnikov basis inKeldysh space. Based on a perturbation expansion in the local interaction $U$,the special form of the interaction vertex allows to write diagrammatic rulesin which vacuum Feynman diagrams directly vanish. This reproduces the mainproperty of the previous algorithm, without the cost of the exponential sumover Keldysh indices. In an importance sampling procedure, this implies thatonly interaction times in the vicinity of the measurement time contribute. Suchan algorithm can then directly address the long-time limit needed in the studyof steady states in out-of-equilibrium systems. We then implement and discussdifferent variants of Monte Carlo algorithms in the Larkin-Ovchinnikov basis. Asign problem reappears, showing that the cancellation of vacuum diagrams has nodirect impact on it.

Cancellation of vacuum diagrams and long-time limit in out-of-equilibrium diagrammatic Quantum Monte Carlo