Spin and current correlation functions in thed-density-wave state of the cuprates

We calculate the spin-spin and current-current correlation functions in states exhibiting $d_{x^2-y^2}$-density wave (DDW) order, $d_{x^2-y^2}$ superconducting order (DSC), or both types of orders. The spin-spin correlation functions in a state with both DDW and DSC orders and in a state with DDW order alone, respectively, illuminate the resonant peak seen in the superconducting state of the underdoped cuprates and the corresponding feature seen in the pseudogap regime. The current-current correlation function in a state with both DDW and DSC order evinces a superfluid density with doping dependence, which is consistent with that of the underdoped cuprates. These calculations strengthen the identification of the pseudogap with DDW order and of the underdoped cuprates with a state with both DDW and DSC orders.