Smeared phase transition in the dissipative random quantum Ashkin-Teller model

We study the effects of dissipation in the phase diagram of the random quantum Ashkin-Teller model by means of a generalization of the strong-disorder renormalization group combined with adiabatic renormalization. This model has three phases and three quantum phase transitions. We demonstrate that the combined effect of Ohmic dissipation and quenched disorder smears two out of the three quantum phase transitions. Our analytical theory allows us to understand why one of the phase transitions remains sharp. This is due to a cancellation of the dissipation effects on the nontrivial nature of the intertwined order parameter of one of the phases.