Evidence for 4D XY Quantum Criticality in $^4$He Confined in Nanoporous Media at Finite Temperatures

TL;DR

This study demonstrates that superfluid helium confined in nanoporous media exhibits quantum critical behavior consistent with the 4D XY universality class at finite temperatures, differing from bulk helium's classical 3D XY behavior.

Contribution

The paper provides the first precise measurement of the critical exponent of superfluid density in nanoporous helium, establishing finite-temperature 4D XY quantum criticality.

Findings

Critical exponent of superfluid density is approximately 1.0.

Finite-temperature superfluid transition belongs to 4D XY universality class.

Quantum critical behavior persists at finite temperatures.

Abstract

$^4$He 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 $^4$He in porous Gelsil glasses with pore size of 3.0 nm using the Helmholtz resonator technique. The critical exponent $\zeta$ of the superfluid density was found to be 1.0 $\pm$ 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 $\zeta$ = 0.67. The quantum critical behavior at a finite temperature is understood by strong phase fluctuation in local Bose-Einstein condensates above the superfluid transition temperature. $^4$He in nanoporous media is a unique example in which quantum criticality emerges not only at 0 K but at finite temperatures.