Simulating nonequilibrium quantum many-body systems remains a major challenge due to the exponential growth of the computational complexity with real time. Here we implement a nonequilibrium impurity solver based on the weak-coupling expansion and the tensor cross interpolation, and apply it to nonequilibrium dynamical mean-field theory (DMFT). The method approximates the integrands of the high-dimensional integrals arising in the weak-coupling expansion in a tensor-train form, enabling efficient evaluations without stochastic sampling and thereby mitigating the sign problem affecting continuous-time quantum Monte Carlo (CT-QMC) methods. Benchmark calculations for an exactly solvable nonequilibrium impurity model agree well with the exact results and reveal a low-rank structure of the integrands. When applied to interaction-quench problems in the half-filled Hubbard model, the method reproduces fast thermalization at a critical interaction strength with accuracy comparable to CT-QMC. Away from half filling, where the sign problem becomes even more severe, the present approach remains well controlled, revealing a crossover instead of a sharply defined fast thermalization point in the 3/4-filled case. The solver can also be applied to steady-state DMFT problems, yielding accurate spectral functions in the metallic regime without analytic continuation.

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• Dynamical phase transitions
• Mott insulators
• Nonequilibrium systems
• Quantum many-body systems
• Strongly correlated systems
• Anderson impurity model
• Dynamical mean field theory
• Hubbard model
• Nonequilibrium Green's function
• Tensor network methods