A refined Eigenstate Thermalisation Hypothesis that evades known counterexamples

The Eigenstate Thermalization Hypothesis (ETH) essentially asserts that an eigenstate of a quantum many-body system is indistinguishable from the microcanonical mixed state at the corresponding energy if measured locally. Any attempt to prove the ETH in this simple (and widely used) formulation would likely stumble at the very first step - defining a class of systems it applies to. There are systems where the ETH is known to be invalid - integrable systems and systems with quantum many-body scars. A precise mathematical definition for quantum many-body integrability remains, however, elusive, despite decades of discussions. The situation is even worse for the scarring phenomenon that has come into focus very recently. Thus one is not able to precisely characterise the set of Hamiltonians where the ETH is invalid. As a consequence, the complementary set of Hamiltonians where the ETH can be valid remains also obscure. In this talk I circumvent this difficulty by proposing a refined version of the ETH. It formalises an intuitive understanding that the integrable and scarred systems are rare exceptional points in the parameter space of many-body Hamiltonians, and a generic perturbation of a Hamiltonoian destroys integrability and scars and restores the validity of the ETH.