Competing Bose-glass physics with disorder-induced Bose-Einstein condensation in the doped S=1 antiferromagnet Ni(Cl1−xBrx)2−4SC(NH2)2 at high magnetic fields

We study the interplay between disorder and interactions for emergent bosonic degrees of freedom induced by an external magnetic field in the Br-doped spin-gapped antiferromagnetic material $\mathrm{Ni}{({\mathrm{Cl}}_{1\ensuremath{-}x}{\mathrm{Br}}_x)}₂\ensuremath{-}4\mathrm{SC}{({\mathrm{NH}}₂)}₂$ ($\mathrm{DTN}X$). Building on nuclear magnetic resonance experiments at high magnetic field [A. Orlova et al., Phys. Rev. Lett. 118, 067203 (2017)], we describe the localization of isolated impurity states, providing a realistic theoretical modeling for $\mathrm{DTN}X$. Going beyond single impurity localization we use quantum Monte Carlo simulations to explore many-body effects from which pairwise effective interactions lead to a (impurity-induced) Bose-Einstein condensation (BEC) revival [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017)]. We further address the question of the existence of a many-body localized Bose-glass (BG) phase in $\mathrm{DTN}X$, which is found to compete with a series of a new kind of BEC regimes made out of the multi-impurity states. The global magnetic field--temperature phase diagram of $\mathrm{DTN}X$ reveals a very rich structure for low impurity concentration, with consecutive disorder-induced BEC minidomes separated by intervening many-body localized BG regimes. Upon increasing the impurity level, multiple mini-BEC phases start to overlap, while intermediate BG regions vanish.