Effective gauge-field theory of the t-J model in the charge-spin separated state and its transport properties -: art. no. 104516

We study the slave-boson t-J model of cuprates with high superconducting transition temperatures, and derive its low-energy effective field theory for the charge-spin separated state in a self-consistent manner. The phase degrees of freedom of the mean field for hoppings of holons and spinons can be regarded as a U(1) gauge field, A(i). The charge-spin separation occurs below a certain temperature, T-CSS, as a deconfinement phenomenon of the dynamics of A(i). Below a certain temperature T-SG (<T-CSS), the spin-gap phase develops as the Higgs phase of the gauge-field dynamics, and A(i) acquires a mass m(A). The effective field theory near TSG takes the form of a Ginzburg-Landau theory of a complex scalar field <lambda> coupled with A(i), where lambda represents d-wave pairings of spinons. Three dimensionality of the system is crucial to realize a phase transition at T-SG. By using this field theory, we calculate the dc resistivity rho. At T>T-SG, rho is proportional to T. At T<T-SG, it deviates downward from the T-linear behavior as <rho>proportional toT{1-c(T-SG(-T))(d)}. When the system is near (but not) two dimensional, due to the compactness of the phase of the field lambda, the exponent d deviates from its mean-field value 1/2 and becomes a nonuniversal quantity which depends on temperature and doping. This significantly improves the comparison with the experimental data.