Thermal Conductivity and the Boson Mass in the Bose-Einstein Condensate compound NiCl$_{2}$-4SC(NH$_{2})_{2}$

The quantum magnet NiCl$_{2}$-4SC(NH$_{2})_{2}$ has been shown to exhibit Bose-Einstein Condensation (BEC) of the Ni S = 1 spin system. This compound exhibits field-induced XY antiferromagnetism for magnetic fields along the tetragonal c-axis between H$_{c1}$ = 2.1 and H$_{c2}$ = 12.6 T, and the axial symmetry of the spin environment allows us to understand the quantum phase transitions at H$_{c1}$ and H$_{c2}$ in terms of Bose-Einstein condensation (BEC) of spins. Here the tuning parameter for BEC transition is the magnetic field and not the temperature. It turns out that mass of the bosons that condense can be strongly suppressed by quantum fluctuations, and this effect occurs disproportionately at H$_{c1}$. Here we present new thermal conductivity and specific heat data to probe the effect of quantum fluctuations on the boson mass. We compare the experimental results to quantum Monte Carlo simulations and an effective low-energy theory.