  We present rigorous bounds on the thermalization time of the family of
quantum mechanical spin systems known as stabilizer Hamiltonians. The
thermalizing dynamics are modeled by a Davies master equation that arises from
a weak local coupling of the system to a large thermal bath. Two temperature
regimes are considered. First we clarify how in the low temperature regime, the
thermalization time is governed by a generalization of the energy barrier
between orthogonal ground states. When no energy barrier is present the
Hamiltonian thermalizes in a time that is at most quadratic in the system size.
Secondly, we show that above a universal critical temperature, every stabilizer
Hamiltonian relaxes to its unique thermal state in a time which scales at most
linearly in the size of the system. We provide an explicit lower bound on the
critical temperature. Finally, we discuss the implications of these result for
the problem of self-correcting quantum memories with stabilizer Hamiltonians.
