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

We review our study of critical phenomena in superfluid $^4$He confined in nanoporous glasses. $^4$He in nanoporous media is an ideal ground to survey the quantum phase transition of bosons. In the present work, critical phenomena were examined using a newly developed hydrodynamic mechanical resonator. The critical exponent of superfluid density $\zeta$ was found to be 1.0, in contrast to 0.67 in bulk $^4$He. We also demonstrate that the superfluid density 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 XY criticality, which should have been observed only at 0 K, at finite temperatures. We propose a mechanism of the quantum criticality at finite temperatures in terms of phase alignment among the nanoscale localized Bose condensates (LBECs) in nanopores. The proposed mechanism are discussed in the consideration of the correlation length compared with the quantum effect.