  We theoretically investigate the T-B phase diagram of cuprates building on
the SU(2) pseudogap order recently obtained from the spin-fermion model. At low
temperatures, our analysis reveals an almost temperature-independent critical
magnetic field B_{QDW} at which d-wave superconductivity switches to the
quadrupole density wave (QDW) phase. For temperatures beyond a certain value of
the order of the zero-field superconducting transition temperature T_c, the
critical field B_{QDW}(T) sharply grows. We compare our results derived within
the effective SU(2) non-linear sigma-model with the phase diagram recently
obtained by sound velocity measurements by LeBoeuf et al. [Nat. Phys. 9, 79
(2013)].
