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

## TL;DR

This paper reformulates a real-time diagrammatic Quantum Monte Carlo method in the Larkin-Ovchinnikov basis, enabling efficient long-time limit calculations for out-of-equilibrium steady states, while analyzing the impact on the sign problem.

## Contribution

It introduces a new formulation of the Quantum Monte Carlo algorithm that simplifies vacuum diagram cancellation and addresses long-time limits in out-of-equilibrium systems.

## Key findings

- Vacuum diagrams vanish directly in the new formulation.
- The algorithm efficiently targets interaction times near measurement.
- The sign problem persists despite vacuum diagram cancellation.

## Abstract

We express the recently introduced real-time diagrammatic Quantum Monte Carlo, Phys. Rev. B 91, 245154 (2015), in the Larkin-Ovchinnikov basis in Keldysh space. Based on a perturbation expansion in the local interaction $U$, the special form of the interaction vertex allows to write diagrammatic rules in which vacuum Feynman diagrams directly vanish. This reproduces the main property of the previous algorithm, without the cost of the exponential sum over Keldysh indices. In an importance sampling procedure, this implies that only interaction times in the vicinity of the measurement time contribute. Such an algorithm can then directly address the long-time limit needed in the study of steady states in out-of-equilibrium systems. We then implement and discuss different variants of Monte Carlo algorithms in the Larkin-Ovchinnikov basis. A sign problem reappears, showing that the cancellation of vacuum diagrams has no direct impact on it.