Quantum simulating floating phase and S = ½ critical behavior with S = 1 spin centers with anisotropy in solid-state materials

We propose a novel platform for creating quantum simulators by implanting S = 1 spin centers in solid-state materials. We show that with anisotropy and Zeeman splitting, a 1-d chain of S = 1 spin centers that interact through the magnetic dipole-dipole interaction can be mapped to a S = ½ XYZ + H Heisenberg spin chain. This Hamiltonian can then be tuned by changing the orientation of the chain with respect to the symmetry axes of the spin centers and by varying a small external magnetic field. The phase diagram for this system is rich with critical behavior and shows regions with a critical floating phase, an isotropic Heisenberg model, and a transverse Ising universality class. This system can be used to quantum simulate critical behavior seen in unique S = ½ XYZ + H spin chains and is the first quantum simulator for the floating phase with spin centers in solid-state materials.