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

TL;DR

This study investigates quantum critical phenomena of superfluid helium-4 confined in nanoporous media, revealing 4D XY criticality at finite temperatures through novel hydrodynamic resonator measurements.

Contribution

It provides experimental evidence of 4D XY quantum criticality at finite temperatures in nanoporous helium-4, a phenomenon previously thought observable only at absolute zero.

Findings

Superfluid density critical exponent $z$ is 1.0, differing from bulk helium.

Superfluid density scales as $|P - P_c|^{z_p}$ with z_p=1 at finite temperatures.

Evidence supports the existence of 4D XY criticality at finite temperatures.

Abstract

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.