Thermalization in non-disordered systems

Question

The eigenstate thermalization hypothesis explains the mechanism of the thermalization of generic many-body quantum systems. The presence of disorder, on the other hand, provides an elegant example of many-body quantum properties that fail to thermalize and thus violates the ETH. I am wondering if there are quantum systems that violate ETH without disorder?

Comments

Many-electron atoms will do?

Answer 1

Yes, there are many-body quantum systems that are not disordered, but which also violate ETH. Perhaps the most prominent examples are Bethe-Ansatz integrable systems (mentioned prominently in this review). 

However, all such examples of many-body systems without disorder which do not obey ETH are, to my knowledge, finely tuned. That is to say, if H is clean and fails to satisfy ETH, then I expect (and I don't think I'm alone) that ETH will start to hold if you add small perturbations to H which are local, translation invariant, and sufficiently generic. I don't know of any rigorous results backing up this expectation...so it might not be correct! But that would be surprising.