Probing off-diagonal eigenstate thermalization with tensor networks

Energy filter methods in combination with quantum simulation can efficiently access the properties of quantum many-body systems at finite energy densities S. Lu , . Classically simulating this algorithm with tensor networks can be used to investigate the microcanonical properties of large spin chains, as recently shown by Y. Yang . Here we extend this strategy to explore the properties of off-diagonal matrix elements of observables in the energy eigenbasis, fundamentally connected to the thermalization behavior and the eigenstate thermalization hypothesis. We test the method on integrable and nonintegrable spin chains of up to 60 sites, much larger than accessible with exact diagonalization. Our results allow us to explore the scaling of the off-diagonal functions with the size and energy difference, and to establish quantitative differences between integrable and nonintegrable cases. Published by the American Physical Society 2024