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. an eigenstate (or an equilibrium ensemble) of some pre-quench Hamiltonian H serves as initial condition which then evolves in time according to some post-quench Hamiltonian H ( p ). Absence of thermalization is analytically demonstrated for a large class of quite common pre- and post-quench spin Hamiltonians. The main requirement is that the pre-quench Hamiltonian must exhibit a Z (2) (spin-flip) symmetry, which would be spontaneously broken in the thermodynamic limit, though we actually focus on finite (but large) systems. On the other hand, the post-quench Hamiltonian must violate the Z (2) symmetry, but for the rest may be non-integrable and may obey the eigenstate thermalization hypothesis for (sums of) few-body observables.