= Field-induced triplon condensation
{title2=$\eta(H_c-H_g)=\nu n$}
A <magnetic field> can close the lowest gap of a dilute bosonic triplet branch. In a shifted-parabola model with actual <chemical potential> zero, $\epsilon_k=\hbar^2k^2/(2m)+\nu n-\eta(H-H_g)$ and repulsion $\nu>0$ prevent indefinite <density> growth. The normal minimum reaches zero when $\eta(H_c-H_g)=\nu n$. At that point the finite thermal excited population saturates and macroscopic ground-state occupation can develop.
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