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Monte Carlo determination of the critical exponents for a quantum phase transition of a dimerized spin-1/2 Heisenberg model

We simulate the spin-1/2 Heisenberg model with a spatially staggered anisotropy using first principles Monte Carlo method. In particular, the critical exponents $β/ν$ and $ω$ associated with the quantum phase transition induced by dimerization are determined with high precision. Here $β$ and $ν$ are the exponents related to the magnetization and the correlation length, respectively. In addition, $ω$ is the confluent exponent. With very accurate data of the relevant observables, we first obtain a value of $ω$ compatible with the known result in the O(3) universality class. Further, using either the value of $ω$ determined here or the established one in the literature, the exponent $β/ν$ calculated from our data is in quantitative agreement with the known result $β/ν= 0.519(1)$ as well. Our investigation suggests that the quantum phase transition studied here is fully consistent with the O(3) universality class.