Thermalization dynamics close to a quantum phase transition.

We investigate the dissipative dynamics of a quantum critical system in contact with a thermal bath, focusing on the response of the system to a sudden change of the bath temperature, in analogy to studies of aging. The specific example of the XY model in a transverse magnetic field whose spins are locally coupled to a set of bosonic baths is considered. We analyze the spin-spin correlations and block correlations and identify some universal features in the out-of-equilibrium dynamics. Two distinct regimes, characterized by different time and length scales, emerge. The initial transient dynamics is characterized by the same critical exponents as those of the equilibrium quantum phase transition and resembles the dynamics of thermal phase transitions. At long times equilibrium is reached through the propagation along the chain of a thermal front in a manner similar to the classical Glauber dynamics.