The self-energy encodes the fundamental lifetime of quasiparticle excitations. In one dimension, it is known to display anomalous behavior at zero temperature for interacting fermions, reflecting the breakdown of Fermi-liquid theory. Here we show that the self-energy is also anomalous in the infinite-temperature Hubbard chain, where thermal fluctuations are maximal. Focusing on the second-order ring diagram, we find that the imaginary part of the self-energy diverges nonperturbatively: as a power law with exponent $-1/3$ near half filling, and logarithmically away from it. These divergences are captured numerically by the anomalous temporal relaxation of the Green's function and the composite fermion spectral function. Our results demonstrate that anomalous relaxation and the breakdown of perturbation theory survive even at maximal entropy, which can be observed in cold-atom experiments probing the Hubbard chain at high temperatures.

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• 1-dimensional systems
• Strongly correlated systems
• Hubbard model