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

Abstract

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, \(T_{\rm CSS}\), as a deconfinement phenomenon of the dynamics of \(A_i\). Below certain temperature \(T_{\rm SG} (< T_{\rm CSS})\), 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 \(T_{\rm SG}\) takes the form of 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 \(T_{\rm SG}\). By using this field theory, we calculate the dc resistivity \(\rho\). At \(T > T_{\rm SG}\), \(\rho\) is proportional to \(T\). At \(T < T_{\rm SG}\), it deviates downward from the \(T\)-linear behavior as \(\rho \propto T \{1 -c(T_{\rm SG}-T)^d \}\). 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.