Quantum simulation of floating phase and S = 1/2 critical behavior using spin solid-state spin centers*

We propose the first quantum simulator for the critical floating phase in solid-state materials. We have mapped a 1-d array of S = 1 spin centers with anisotropy, interacting through the magnetic dipole-dipole interaction, to a S = 1/2 XYZ+H spin chain. Spin chains have long been studied for their rich phase diagrams and accordingly, we find that in addition to the incommensurate critical floating phase, our system can be tuned to an Ising antiferromagnetic phase and Heisenberg spin chain. Additional critical behaviors found in the system include Berezinskii-Kosterlitz-Thouless, Pokrovsky-Talapov, and SU(2) symmetric Heisenberg points. These quantum phases and critical phenomena can be controlled via magnetic fields and the orientational displacement of the spin chain. Our work shows the potential of solid-state spin chains as quantum simulators, and with the active development of more powerful and longer range spin-spin interactions between spin centers mediated by bosonic modes, solid-state spin chains are promising quantum simulators for a variety of exotic quantum phases and critical behaviors.