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Motivated by the numerical simulation of systems which display quantum phasetransitions, we present a novel application of the meron-cluster algorithm tosimulate the quantum antiferromagnetic Heisenberg model coupled to an externaluniform magnetic field both in one and in two dimensions. In the infinitevolume limit and at zero temperature we found numerical evidence that supportsa quantum phase transition very close to the critical values $B_{c}=2$ and$B_{c}=4$ for the system in one and two dimensions, respectively. For the onedimensional system, we have compared the numerical data obtained withanalytical predictions for the magnetization density as a function of theexternal field obtained by scaling-behaviour analysis and Bethe Ansatztechniques. Since there is no analytical solution for the two dimensional case,we have compared our results with the magnetization density obtained by scalingrelations for small lattice sizes and with the approximated thermodynamicallimit at zero temperature guessed by scaling relations. Moreover, we havecompared the numerical data with other numerical simulations performed by usingdifferent algorithms in one and two dimensions, like the directed loop method.The numerical data obtained are in perfect agreement with all these previousresults, which confirms that the meron-algorithm is reliable for quantum MonteCarlo simulations and applicable both in one and two dimensions. Finally, wehave computed the integrated autocorrelation time to measure the efficiency ofthe meron algorithm in one dimension.

Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions