Symmetry-prohibited thermalization after a quantum quench

The observable long-time behavior of an isolated many-body system after a quantum quench is considered, i.e., eigenstate (or equilibrium ensemble) some pre-quench Hamiltonian $H$ serves as initial condition which then evolves in time according to post-quench $H_p$. Absence thermalization analytically demonstrated for large class quite common pre- and spin Hamiltonians. main requirement that the must exhibit $Z_2$ (spin-flip) symmetry, would be spontaneously broken thermodynamic limit, though we actually focus on finite (but large) systems. On other hand, violate but rest may non-integrable obey hypothesis (sums of) few-body observables.