Effective gauge field theory of the t-J model in the charge-spin separated state and its transport properties

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 certain temperature, T CSS , as a deconfinement phenomenon of the dynamics of A i . Below 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 T SG takes the form of Ginzburg-Landau theory of a complex scalar field λ coupled with A i , where λ 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 ρ . At T > T SG , ρ is proportional to T . At T < T SG , it deviates downward from the T -linear behavior as ρ ∝ T { 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 λ , 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.