  In this work we propose a novel solid-state platform for creating quantum
simulators based on implanted spin centers in semiconductors. We show that
under the presence of an external magnetic field, an array of $S=1$ spin
centers interacting through magnetic dipole-dipole interaction can be mapped
into an effective spin-half system equivalent to the XYZ model in an external
magnetic field. Interestingly, this system presents a wide range of quantum
phases and critical behaviors that can be controlled via magnetic field and
orientational arrangement of the spin centers. We demonstrate our interacting
spin chain can be tuned to both isotropic Heisenberg model and transverse-field
Ising universality class. Notably, our model contains a line where the system
is in a critical floating phase that terminates at
Berezinskii-Kosterlitz-Thouless and Pokrovsky-Talapov transition points. We
propose this system as the first solid-state quantum simulator for the floating
phase based on spin centers.
