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Magnetic monopoles are suggested to play an important role in stronglycoupled quark-gluon plasma (sQGP) near the deconfinement temperature. So far,their many-body treatment has only been done classically, with just binaryscattering solved in quantum mechanics. In this paper we start quantummany-body studies of the monopole ensembles. Specifically, we carry outnumerical simulations of the path integral for one- and two-component CoulombBose systems. We determine the relation between the critical temperature forthe Bose-Einstein condensation phase transition $T_\text{c}$ and the Coulombcoupling strength using two methods, the classic finite-size scaling of thecondensate and a lattice-tested method based on permutation cycles. For aone-component Coulomb Bose gas, we observe the same behavior of the criticaltemperature -- initially rising slightly then falling as interaction strengthis increased -- as seen in the case of hard spheres; we also observe the samebehavior for a two-component Coulomb Bose gas. We then calculate sets of radialcorrelation functions between the like and unlike charged particles. Bymatching those with the correlation functions previously calculated on thelattice, we derive an effective quantum model of color magnetic monopoles inQCD. From this matched model, we are able to extract the monopole contributionto QCD equation of state near $T_\text{c}$.

Effective Model of QCD Magnetic Monopoles From Numerical Study of One- and Two-Component Coulomb Quantum Bose Gases