Quantum contact process on scale-free networks

The quantum contact process (QCP), a combination of the quantum coherent and classical incoherent processes, exhibits a quantum absorbing phase transition (QAPT). Most studies of the QCP have focused on the case in which active states are induced by the s-excited state of Rydberg atoms. Thus, quantum coherence is induced by short-range interactions. In this case, a QAPT in one dimension is second-order. However, when active states are induced by the d-excited state, long-range interactions must be considered. In this case, even in one dimension, a discontinuous transition occurs. Thus, the type of QAPT depends on interaction range. Here, we aim to investigate how the QAPT depends on embedded structure and thus consider the QCP model on scale-free (SF) networks, in which the degree distribution follows a power law Pd(k) ~ k−λ and the mean distance between two nodes depends on system size N logarithmically. Thus, we can find how the QAPT depends on interaction range and the heterogeneity of the number of connections simultaneously. We find analytically that various types of QAPTs emerge depending on the degree exponent λ. Finally, we compare the properties of the PT of the QCP with those of its classical counterparts.