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Spin squeezing, as a crucial quantum resource, plays a pivotal role inquantum metrology, enabling us to achieve high-precision parameter estimationschemes. Here we investigate the spin squeezing and the quantum phasetransition in an anisotropic central spin system. We find that this kind ofcentral spin systems can be mapped to the anisotropic Lipkin-Meshkov-Glickmodel in the limit where the ratio of transition frequencies between thecentral spin and the spin bath tends towards infinity. This property can inducea one-axis twisting interaction and provides a new possibility for generatingspin squeezing. We separately consider generating spin-squeezed states via theground state and the dynamic evolution of the central spin model. The resultsshow that the spin squeezing parameter improves as the anisotropy parameterdecreases, and its value scales with system size as $N^{-2/3}$. Furthermore, weobtain the critical exponent of the quantum Fisher information around thecritical point by numerical simulation, and find its value tends to $4/3$ asthe frequency ratio and the system size approach infinity. This work offers apromising scheme for generating spin-squeezed state and paves the way forpotential advancements in quantum sensing.

Spin squeezing generated by the anisotropic central spin model