Low temperature thermodynamics of multi-flavored hardcore bosons by the Br\"uckner approach

Dynamic correlations of quantum magnets provide valuable information. However, especially at finite temperature, many observations, e.g., by inelastic neutron scattering experiments, are not yet quantitatively understood. Generically, the elementary excitations of gapped quantum magnets are hardcore bosons because no two of them can occupy the same site. The previously introduced diagrammatic Br\"uckner approach dealt with hardcore bosons of a single flavor at finite temperature. Here, this approach is extended to hardcore bosons of several kinds (flavors). The approach based on ladder diagrams is gauged with so far unknown rigorous results for the thermal occupation function of multiflavored hardcore bosons in one dimension with nearest-neighbor hopping. For low temperatures, it works very well. Furthermore, we study to which extent the approach is a conserving approximation. Empirical evidence shows that this is true only in the single-flavor case.