We demonstrate the versatility, simplicity, and power of the minimally augmented spin-wave theory in studying phase diagrams of the quantum spin models in which unexpected magnetically ordered phases occur or the existing ones expand beyond their classical stability regions. We use this method to obtain approximate phase diagrams of the two paradigmatic spin-
21 models on the honeycomb lattice: the ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ ferro-antiferromagnetic and ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ antiferromagnetic
XXZ models. For the ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ case, various combinations of the
XXZ anisotropies are analyzed. In a dramatic deviation from their classical phase diagrams, which host significant regions of the noncollinear spiral phases, quantum fluctuations stabilize several unconventional collinear phases and significantly extend conventional ones to completely supersede spiral states. These results are in close agreement with the available density-matrix renormalization group calculations. The applicability of this approach to the other models and its potential extension to different types of orders are discussed.
We numerically investigate mixtures of two interacting bosonic species with unequal parameters in one-dimensional optical lattices. In large parameter regions full phase segregation is seen to minimize the energy of the system, but the true ground state is masked by an exponentially large number of metastable states characterized by microscopic phase separation. The ensemble of these quantum emulsion states, reminiscent of emulsions of immiscible fluids, has macroscopic properties analogous to those of a Bose glass, namely, a finite compressibility in absence of superfluidity. Their metastability is probed by extensive quantum Monte Carlo simulations generating rich correlated stochastic dynamics. The tuning of the repulsion of one of the two species via a Feshbach resonance drives the system through a quantum phase transition to the superfluid state.