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We review our study of critical phenomena in superfluid $^4$He confined innanoporous glasses. $^4$He in nanoporous media is an ideal ground to survey thequantum phase transition of bosons. In the present work, critical phenomenawere examined using a newly developed hydrodynamic mechanical resonator. Thecritical exponent of superfluid density $\zeta$ was found to be 1.0, incontrast to 0.67 in bulk $^4$He. We also demonstrate that the superfluiddensity is proportional to $|P - P_{\mathrm c}|^{\zeta_p}$ with $\zeta_p = 1$at any finite temperatures. These are the decisive evidences for the 4D XYcriticality, which should have been observed only at 0 K, at finitetemperatures. We propose a mechanism of the quantum criticality at finitetemperatures in terms of phase alignment among the nanoscale localized Bosecondensates (LBECs) in nanopores. The proposed mechanism are discussed in theconsideration of the correlation length compared with the quantum effect.

$^4$He in Nanoporous Media: 4D XY Quantum Criticality at Finite Temperatures