Decoherence in the quantum Ising model with transverse dissipative interaction in the strong coupling regime

We study the decoherence dynamics of a quantum Ising lattice of finite size with a transverse dissipative interaction, namely the coupling with the bath is assumed perpendicular to the direction of the spins interaction and parallel to the external transverse magnetic field. In the limit of small transverse field, the eigenstates and spectrum are obtained by a strong coupling expansion, from which we derive the Lindblad equation in the Markovian limit. At temperature lower than the energy gap and for weak dissipation, the decoherence dynamics can be restricted to take only the two degenerate ground states and the first excited subspace into account. The latter is formed by pairs of topological excitations (domain walls or kinks), which are quantum delocalized along the chain due to the small magnetic field. We find that some of these excited states form a relaxation-free subspace, i.e. they do not decay to the ground states. We also discuss the decoherence dynamics for an initial state formed by a quantum superposition of the two degenerate ground states corresponding to the orthogonal classical, ferromagnetic states.