Four-dimensional XY quantum critical behavior of 4He in nanoporous media

The superfluid transition in liquid He4 filled in Gelsil glass observed in recent experiments is discussed in the framework of quantum critical phenomena. We show that quantum fluctuations of phase are indeed important in the experimentally studied temperature range owing to the small pore size of Gelsil, in contrast to He4 filled in previously studied porous media such as Vycor glass. As a consequence of an effective particle-hole symmetry, the quantum critical phenomena of the system are described by the four-dimensional XY universality class, except in the immediate vicinity of the quantum critical point, and the resulting simple scaling agrees with the experimental data remarkably well.