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

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