  In quantum statistical mechanics, closed many-body systems that do not
exhibit thermalization after an arbitrarily long time in spite of the presence
of interactions are called as many-body localized systems, and recently have
been vigorously investigated. After a brief review of this topic, we consider a
many-body interacting quantum system in one dimension, which has conformal
symmetry and integrability. We exactly solve the system and discuss its thermal
or non-thermal behavior.
