  In this paper, we formulate and quantitatively examine the effect of
dissipation on topological systems. We use a specific model of Kitaev quantum
wire with an onsite Ohmic dissipation, and perform a numerically exact quantum
Monte Carlo simulation to investigate this interacting open quantum system with
a strong system-bath (SB) coupling beyond the scope of Born-Markovian
approximation. We concentrate on the effect of dissipation on the topological
features of the system (e.g. the Majorana edge mode) at zero temperature, and
find that even though the topological phase is robust against weak SB couplings
as it is supposed to be, it will eventually be destroyed by sufficiently strong
dissipations via either a continuous quantum phase transition or a crossover
depending on the symmetry of the system. The dissipation-driven quantum
criticality is also discussed. In addition, using the framework of Abelian
bosonization, we provide an analytical description of the interplay between
pairing, dissipation and interaction in our model.
