Quantum critical Bose gas in the two-dimensional limit in the honeycomb antiferromagnet YbCl$_3$ under magnetic fields

BEC is a quantum phenomenon, where a macroscopic number of bosons occupy the lowest energy state and acquire coherence at low temperatures. It is realized not only in $^4$He and dilute atomic gases, but also in quantum magnets, where hardcore bosons, introduced by the Matsubara-Matsuda transformation of spins, condense. In 3D antiferromagnets, an XY-type long-range ordering (LRO) occurs near a magnetic-field-induced transition to a fully polarized state (FP) and has been successfully described as a BEC in the last few decades. An attractive extension of the BEC in 3D magnets is to make their 2D analogue. For a strictly 2D system, BEC cannot take place due to the presence of a finite density of states at zero energy, and a Berezinskii-Kosterlitz-Thouless (BKT) transition may instead emerge. In a realistic quasi-2D magnet consisting of stacked 2D magnets, a small but finite interlayer coupling stabilizes marginal LRO and BEC, but such that 2D physics, including BKT fluctuations, is still expected to dominate. A few systems were reported to show such 2D-limit BEC, but at very high magnetic fields that are difficult to access. The honeycomb $S$ = 1/2 Heisenberg antiferromagnet YbCl$_3$ with an intra-layer coupling $J\sim$ 5 K exhibits a transition to a FP state at a low in-plane magnetic field of $H_{\rm s}$ = 5.93 T. Here, we demonstrate that the LRO right below $H_{\rm s}$ is a BEC in the 2D-limit stabilized by an extremely small interlayer coupling $J_{\perp}$ of 10$^{-5}J$. At the quantum critical point Hs, we capture 2D-limit quantum fluctuations as the formation of a highly mobile, interacting 2D Bose gas in the dilute limit. A much-reduced effective boson-boson repulsion Ueff as compared with that of a prototypical 3D system indicates the presence of a logarithmic renormalization of interaction unique to 2D.