Functional Renormalization Group Study of Correlated Bose-Einstein Systems -- Low-Temperature Properties of Specific Heat

Greywall's measurement[1] on the specific heat of the superfluid ⁴He exhibit deviations from the T³-law predicted by the Landau theory. This system belongs to the Bose-Einstein condensates (BECs) where correlations are strong.
Recently, one of the authors derived the renormalization group equations for correlated BECs based on the vertex expansion of the effective action[2]. A notable feature of this formalism is that we can avoid the infrared divergence systematically, and the existence of a gapless mode is also guaranteed since it satisfies Goldstone's theorem I (or Hugenholtz-Pines theorem)[3]. On the basis of this formulation, it has been shown that the single-particle excitations of homogeneous BECs at finite temperatures should deviate eventually as the wavenumber k approaches 0 from the linear dispersion predicted by Bogoliubov theory, which can be the origin of the Greywall's experiment result above.
In this talk, we report the numerical results on the specific heat of superfluid ⁴He obtained by solving the functional renormalization group equations. We will also discuss the effective mass of the single-particle excitation.

[1]D. S. Greywall, Phys. Rev. B 18, 2127 (1978).
[2]T. Kita, J. Phys. Soc. Jpn. 88, 054003 (2019).
[3]T. Kita, J. Phys. Soc. Jpn. 80, 084606 (2011).