Analog quantum simulation of commensurate-incommensurate phase transitions using spin solid-state spin centers

Spin chains have long been studied for their rich phase diagrams and exotic behaviors, and subsequently, a fully tunable spin chain is a desirable analog quantum simulator. Previously, it hasn’t been feasible to engineer spin chains with spin centers due to nanometer separations being required for them to strongly interact. However, proposals to engineer strong, long-range interactions between spin centers with bosonic modes as mediators have the potential to address this limitation and make solid-state spin center arrays a promising novel platform for analog quantum simulation. We have previously shown that a model for a 1-d array of S=1spin centers with anisotropy, interacting through the magnetic dipole-dipole interaction, contains two lines of critical floating phases that each terminates in Berezinskii-Kosterlitz-Thouless (BKT) and Pokrovsky-Talapov points. We have expanded upon this work to identify lines of BKT and Pokrovsky-Talapov points that arise for various configurations of applied magnetic fields and orientations of the spin chain within its crystal host. BKT points can be challenging to locate in certain finite-sized systems, so we employ several methods, such as using predictions from conformal field theorists to extract the Luttinger liquid exponent with crosscap states, in hopes of precisely locating the BKT lines.