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Charge dynamics in an ideal cuprate $Ca_{2-x} Na_x Cu O_2 Cl_2$: optical conductivity from Yang-Rice-Zhang ansatz

We theoretically investigate charge dynamics in weakly coupled $CuO_2$ planes of the cuprate $Ca_{2-x} Na_x Cu O_2 Cl_2$ (CNCOC) using Kubo formula for optical conductivity in the underdoped regime. The spectral function needed in Kubo formula is obtained from an analytical form of electron Green's function proposed (ansatz) by Yang-Rice-Zhang (YRZ) for the underdoped cuprates based on their previous renormalized mean field theory and on the investigations of weakly coupled Hubbard ladders. Although to an unaided eye the results of the numerical calculation look very similar to that found experimentally in [K. Waku etal. 2004] but a careful examination with extended Drude formalism shows that YRZ ansatz for the calculation of optical conductivity is not sufficient to understand the charge dynamics in $CuO_2$ planes of the cuprate CNCOC. More physics is needed especially electromagnetic response from bound charges.