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

Effect of magnetic field on competition between superconductivity and charge order below the pseudogap state