The shape phase transition for certain isotope or isotone chains, associated with the quantum phase transition of finite nuclei, is an intriguing phenomenon in nuclear physics. A notable case is the Xe isotope chain, where the structure transits from a $\gamma$-soft rotor to a spherical vibrator, with the second-order shape phase transition occurring in the vicinity of ${}^{128–130}\mathrm{Xe}$. In this Letter, we focus on investigating the $\gamma$-soft deformation of ${}^{129}\mathrm{Xe}$ associated with the second-order shape phase transition by constructing novel correlators for ultrarelativistic ${}^{129}\mathrm{Xe}+{}^{129}\mathrm{Xe}$ collisions. In particular, our iEBE-VISHNU model calculations show that the correlation between elliptic flow $v_2$ and mean transverse momentum $[p_T]$, denoted as ${\rho }_2$, as well as the $[p_T]$ fluctuation ${\mathrm{\Gamma }}_{p_T}$, which were previously used to claim the evidence of the rigid triaxial deformation of ${}^{129}\mathrm{Xe}$, can also be well explained by the $\gamma$-soft deformation of ${}^{129}\mathrm{Xe}$. We further propose two novel correlators ${\rho }_{4,2}$ and ${\rho }_{2,4}$, which carry nontrivial higher-order correlations and show unique capabilities to distinguish between the $\gamma$-soft and the rigid triaxial deformation of ${}^{129}\mathrm{Xe}$ in ${}^{129}\mathrm{Xe}+{}^{129}\mathrm{Xe}$ collisions at the LHC. The present study provides a novel way to explore the second-order shape phase transition of finite nuclei with ultrarelativistic heavy ion collisions.

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• Collective flow
• Hydrodynamic models
• Nuclear shapes and moments
• Particle correlations & fluctuations