We present a detailed study of the real-time dynamics and spectral properties of the one-dimensional fermionic Hubbard model at infinite temperature. Using tensor network simulations in Liouville space, we compute the single-particle Green's function and analyze its dynamics across a broad range of interaction strengths. To complement the time-domain approach, we develop a high-resolution Chebyshev expansion method within the density matrix formalism, enabling direct access to spectral functions in the frequency domain. As interactions are introduced, a transition in the spectral function from a sharp, free-particle dispersion to a broadened two-band structure associated with hole and electron excitations is observed, and electron propagators are found to display a diffusive falloff. At infinite interaction strength ($U=\infty$), we exploit a determinant representation of the Green's function to access both real-time and spectral properties. In this regime, spectral functions retain a blurred, cosinelike momentum dispersion in frequency space indicating almost coherent propagation, while the dynamics display nontrivial light-cone spreading with an anomalous exponent $\alpha \approx 0.78$. Our results demonstrate that strong correlations and nontrivial quantum coherence can persist even at infinite temperature and infinite interaction strength.

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• 1-dimensional systems
• Hubbard model
• Tensor network methods