Renormalisation-group approach to a Bose System below the critical temperature

G. Benfatto

Felipe Isaule, Ivan Morera

We provide a detailed presentation of the functional renormalisation group (FRG) approach for weakly-interacting Bose–Bose mixtures, including a complete discussion on the RG equations. To test this approach, we examine thermodynamic properties of balanced three-dimensional Bose–Bose gases at zero and finite temperatures and find a good agreement with related works. We also study ground-state energies of repulsive Bose polarons by examining mixtures in the limit of infinite population imbalance. Finally, we discuss future applications of the FRG to novel problems in Bose–Bose mixtures and related systems.

K. K. Singh

Boris Krippa

Zero-temperature binary Bose mixtures with mass and intraspecies couplings imbalances are studied using the functional renormalisation group (FRG) framework. We find that this dual asymmetry induces a spontaneous redistribution of quantum fluctuations between the components. This effect leads to a significant divergence in the quasiparticle residues of the two species, a phenomenon not captured in mean-field treatments. Critically, our FRG analysis predicts a systematic reduction of the density-channel sound velocity with increasing asymmetry -- a result that qualitatively contradicts the behaviour predicted by standard Bogoliubov theory. The ratio of the renormalisation factors is proposed as a robust quantitative probe of many-body correlations and fluctuation transfer. These findings provide a consistent non-perturbative framework for interpreting future experiments on heterogeneous mixtures.

W. Reich

A real space renormalisation group method has been applied to find the critical temperature of the Ising model on cubic and octahedral lattices. The result obtained for a cubic lattice is in good agreement with that obtained from high-temperature series expansion and is better than the results of other papers. A modification of the transformation tested for a simple cubic lattice allowed the authors to find the critical temperature for an octahedral lattice. The latter has not so far been studied by any version of the real space renormalisation group method.

Attilio L. Stella, Flavio Toigo