Parametrically　driven　nonlinear　resonators　represent　a　building　block　for　realizing　fault-tolerant　quantum　computation　and　are　useful　for　critical　quantum　sensing.　From　a　fundamental　viewpoint,　the　most　intriguing　feature　of　such　a　system　is　perhaps　the　critical　phenomena,　which　can　occur　without　interaction　with　any　other　quantum　system.　The　non-analytic　behaviors　of　its　eigenspectrum　have　been　substantially　investigated,　but　those　associated　with　the　ground　state　wavefunction　have　largely　remained　unexplored.　Using　the　quantum　ground　state　geometric　tensor　as　an　indicator,　we　comprehensively　establish　a　phase　diagram　involving　the　driving　parameter　ε　and　phase　ϕ.　The　results　reveal　that　with　the　increase　in　ε,　the　system　undergoes　a　quantum　phase　transition　from　the　normal　to　the　symmetry-breaking　phase,　with　the　critical　point　unaffected　by　ϕ.　Furthermore,　the　critical　exponent　and　scaling　dimension　are　obtained　by　an　exact　numerical　method,　which　is　consistent　with　previous　works.　Our　numerical　results　show　that　the　phase　transition　falls　within　the　universality　class　of　the　quantum　Rabi　model.　This　work　reveals　that　the　quantum　metric　and　Berry　curvature　display　diverging　behaviors　across　the　quantum　phase　transition.　©　2024　Optica　Publishing　Group　under　the　terms　of　the　Optica　Open　Access　Publishing　Agreement.