  Graphene hosting a pair of collinear adatoms in the phantom atom
configuration has pseudogap with cubic scaling on energy,
$\Delta\propto|\varepsilon|^{3}$ which leads to the appearance of
spin-degenerate bound states in the continuum (BICs) [Phys. Rev. B 92, 045409
(2015)]. In the case when adatoms are locally coupled to a single carbon atom
the pseudogap scales linearly with energy, which prevents the formation of
BICs. In this Letter, we explore the effects of non-local coupling
characterized by the Fano factor of interference $q_{0},$ tunable by changing
the slope of the Dirac cones in the graphene band-structure. We demonstrate
that three distinct regimes can be identified: i) for $q_{0}<q_{c1}$ (critical
point) a mixed pseudogap $\Delta\propto|\varepsilon|,|\varepsilon|^{2}$ appears
yielding a phase with spin-degenerate BICs; ii) near $q_{0}=q_{c1}$ when
$\Delta\propto|\varepsilon|^{2}$ the system undergoes a quantum phase
transition in which the new phase is characterized by magnetic BICs and iii) at
a second critical value $q_{0}>q_{c2}$ the cubic scaling of the pseudogap with
energy $\Delta\propto|\varepsilon|^{3}$ characteristic to the phantom atom
configuration is restored and the phase with non-magnetic BICs is recovered.
The phase with magnetic BICs can be described in terms of an effective
intrinsic exchange field of ferromagnetic nature between the adatoms mediated
by graphene monolayer. We thus propose a new type of quantum phase transition
resulting from the competition between the states characterized by
spin-degenerate and magnetic BICs.
