The application of a magnetic field offers a unique way to control a quantum critical point in some systems. For underdoped high temperature cuprate superconductors (HTS), magnetic field suppresses the superconductivity and therefore enhances the order parameters of the competing charge density wave (CDW) and spin density wave (SDW) phases. Here we propose to investigate the effect of a magnetic field on a HTS system which is at the critical doping for the disappearance of SDW order. This will yield a field controlled quantum critical point such that at H=0 and T=0 system is quantum critical. We will investigate how the spin correlations change with T and H as we approach the quantum critical point.