Quantum phase transitions in d-wave superconductors

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Based on an effective Lagrangian obtained from the holon-pair boson theory of Lee and Salk [Phys. Rev. B 64, 052501 (2001)] for high Tc cuprates, we explore physical states involved with quantum phase transitions around a critical hole doping of d-wave superconductivity. We find a new quantum phase transition, a confinement to deconfinement transition for internal gauge charge in the superconducting phase. An antiferro- to para- magnetic transition in the superconducting state is explained in the context of the confinement to deconfinement transition. We obtain effective field theories in each region associated with the phase transitions.