In recent years, quantum dynamics in isolated systems has attracted much attention. In particular, it has been a fundamental problem whether an isolated quantum system exhibits thermalization (approach to thermal equilibrium). It is now recognized that thermal equilibrium state is typical in the sense that an overwhelming majority of pure states with a definite macroscopic energy correspond to thermal equilibrium. Approach to thermal equilibrium is then interpreted as an evolution from an atypical nonequilibrium state to a typical equilibrium state. Although this interpretation is quite natural, typicality of thermal equilibrium does not explain the presence or absence of thermalization in a given system. For example, typicality argument holds in an integrable system, but it fails to thermalize. In order to characterize the presence or absence of thermalization, properties of quantum dynamics should be further investigated.
A plausible scenario of thermalization is the one based on the property called the eigenstate thermalization hypothesis (ETH). The ETH states that every energy eigenstate represents thermal equilibrium. If the ETH is correct, we can generally show thermalization with an additional mild condition on the initial state. Numerically it has been shown that nonintegrable systems satisfy the ETH while integrable systems and many-body localized systems do not. Therefore, the ETH has been regarded as a good characterization of a quantum system exhibiting thermalization.
In this talk, we propose a systematic construction of counterexamples to this scenario. We construct a family of models without the ETH . In particular, constructed models are neither integrable nor many-body localized, so our method gives a novel class of systems violating the ETH. We will show that our model thermalizes after an arbitrary quantum quench from an equilibrium state of another local Hamiltonian at finite temperature . In other words, our model thermalizes for a general class of initial states although the ETH does not hold. It means that the ETH is not a necessary condition of thermalization against conventional beliefs.
 N. Shiraishi and T. Mori, arXiv: 1702.08227
 T. Mori and N. Shiraishi, in preparation.