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    On the tensorial structure of the generalized eigenstate thermalization hypothesis
    (Universidad del Valle, 2025) Campos Muñoz, Krystifer; Madronero, Javier
    In this work, we focus on the Eigenstate Thermalization Hypothesis (ETH) [1] as a leading explanation for the emergence of thermal behavior in many-body quantum systems. We discuss recent advances in the field, particularly the work of Silvia, Laura, and Jorge [2,3], who extended the ETH to include multipoint thermal correlation functions. Their findings revealed a direct connection between these correlations and the cumulants of free probability [4]. This connection, along with the free independence condition, suggests the existence of subleading contributions not captured by the generalized ETH and free probability. To support this idea, we analytically computed the subleading contributions for the two-point correlation functions in a system of random free fermions; for that, we used quantum information and random matrix theory techniques that include quantum channels, Gaussian ensembles and Haar averages. Our results confirmed our initial hypothesis: the subleading contributions contain relevant information about the presence or absence of time-reversal symmetry in the system considered.