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تسجيل مستخدم جديدEvidence for 4D XY Quantum Criticality in $^4$He Confined in Nanoporous Media at Finite Temperatures
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$^4$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.
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$^4$He confined in nanoporous Gelsil glass is a unique, strongly correlated Bose system exhibiting quantum phase transition (QPT) by controlling pressure. Previous studies revealed that the QPT occurs with four - dimensional (4D) XY criticality, whic
h appears in the zero-temperature limit of the superfluid density. However, the $P-T$ phase diagram also suggested that 4D XY nature appears at finite temperatures. Here, we have determined the critical exponent of the superfluid density of $^4$He in two Gelsil samples that have pore diameter to be about 3 nm, using a newly developed mechanical resonator technique. The critical exponent $zeta$ in the powerlaw fitting $rho_{mathrm s} propto left| 1 - T/T_{mathrm c} right| ^{zeta}$, where $T_{mathrm c}$ is the superfluid transition temperature, was found to be 1.0 $pm$ 0.1 for all pressures realized in this experiment, 0.1 $<$ $P$ $<$ 2.4 MPa. This value of $zeta$ gives a decisive evidence that the finite-temperature superfluid transition belongs to 4D XY universality class. The emergence of the 4D XY criticality is explained by the existence of many nanoscale superfluid droplets, the so called localized Bose - Einstein condensates (LBECs), above $T_{mathrm c}$. Due to the large energy cost for $^4$He atoms to move between the LBECs, the phase of the LBEC order parameters fluctuates not only in spatial (3D) but imaginary time ($+1$D) dimensions, resulting in the 4D XY criticality by a temperature near $T_{mathrm c}$, which is determined by the finite size of the system in the imaginary time dimension. Below $T_{mathrm c}$, macroscopic superfluidity grows in the nanopores of Gelsil by the alignment of the phases of the LBEC order parameters. An excess dissipation peak observed below $T_{mathrm c}$ is well explained by this phase matching process.
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