Evidence for 4D XY quantum criticality in ⁴He confined in nanoporous media at finite temperatures

4He confined in nanoporous media is a model Bose system that exhibits quantum phase transition (QPT) by varying pressure. We have precisely determined the critical exponent of the superfluid density of liquid 4He in porous Gelsil glasses with pore size of 3.0 nm using the Helmholtz resonator technique. The critical exponent ζ of the superfluid density was found to be 1.0 ± 0.1 for the pressure range 0.1 < P < 2.4 MPa. This value provides decisive evidence that the finite-temperature superfluid transition belongs to the four-dimensional (4D) XY universality class, in contrast to the classical 3D XY one in bulk liquid 4He, in which ζ = 0.67. The quantum critical behavior at a finite temperature is understood by strong phase fluctuations in local Bose-Einstein condensates above the superfluid transition temperature. 4He in nanoporous media is a unique example in which quantum criticality emerges not only at 0K but at finite temperatures.