  The deep sub-Ohmic spin-boson model shows a longstanding non-Markovian
coherence at low temperature. Motivating to quench this robust coherence, the
thermal effect is unitarily incorporated into the time evolution of the model,
which is calculated by the adaptive time-dependent density matrix
renormalization group algorithm combined with the orthogonal polynomials
theory. Via introducing a unitary heating operator to the bosonic bath, the
bath is heated up so that a majority portion of the bosonic excited states is
occupied. It is found in this situation the coherence of the spin is quickly
quenched even in the coherent regime, in which the non-Markovian feature
dominates. With this finding we come up with a novel way to implement the
unitary equilibration, the essential term of the eigenstate-thermalization
hypothesis, through a short-time evolution of the model.
