The mechanism of the charge-spin separation (CSS) in the t-J model, both in the slave-boson and the slave-fermion representations, is studied in detail from the viewpoint of gauge theory. The dynamics of the composite gauge bosons, i.e., of phase degrees of freedom of mean fields defined on links, is carefully analyzed. The Polyakov-Sussskind theory of the confinement-deconfinement (CD) phase transition plays an essential role in this analysis. As we showed generally in our previous paper, the CSS phase corresponds to the deconfinement phase of gauge theory of the mean field. The quasiparticles here are holons, spinons, and gauge bosons. Across the CD transition, another phase, the electron phase, is realized, which corresponds to the confinement phase of gauge theory. The quasiparticles in this phase are conventional electrons, which may be viewed as bound states of holons and spinons. In this paper, we demonstrate that the two-dimensional t-J model exhibits the phenomenon of CSS below a certain critical temperature
TCD, the CD transition temperature, and calculate
TCD as a function of hole concentration. The most important contribution to the realization of CSS comes from nonrelativistic gapless excitations via screening of confining potential among holons and spinons. Reflecting upon two kinds of mean fields, i.e., in the normal and super channels, the resulting CSS deconfinement phase of the t-J model is further classified into Coulomb and Higgs phases. By applying the Polyakov-Susskind theory, they are described by the spin-ordered phase of the isotropic and of the anisotropic XY spin model, respectively.
We study the slave-boson $t\ensuremath{-}J$ 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,
Ai. The charge-spin separation occurs below a certain temperature,
TCSS, as a deconfinement phenomenon of the dynamics of
Ai. Below a certain temperature
TSG(<TCSS), the spin-gap phase develops as the Higgs phase of the gauge-field dynamics, and
Ai acquires a mass
mA. The effective field theory near
TSG takes the form of a Ginzburg-Landau theory of a complex scalar field $\ensuremath{\lambda}$ coupled with
Ai, where $\ensuremath{\lambda}$ represents d-wave pairings of spinons. Three dimensionality of the system is crucial to realize a phase transition at
TSG. By using this field theory, we calculate the dc resistivity $\ensuremath{\rho}.$ At
T>TSG, $\ensuremath{\rho}$ is proportional to T. At
T<TSG, it deviates downward from the T-linear behavior as $\ensuremath{\rho}\ensuremath{\propto}T{1\ensuremath{-}{c(T}_{\mathrm{SG}}\ensuremath{-}{T)}^{d}}.$ When the system is near (but not) two dimensional, due to the compactness of the phase of the field $\ensuremath{\lambda},$ 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.
The Gaussian fluctuations in slave-boson mean-field theory of the $t\text{\ensuremath{-}}J$ model are analyzed in this paper in the low-doping regime where the superconducting to normal (pseudogap phase) transition is driven by vanishing of bose-condensation amplitude. By eliminating the boson and constraint fields exactly in the linear-response regime, we show that the Gaussian theory describes an unconventional Fermi liquid superconductor where the superconducting to normal transition is a new type of phase transition characterized by a change of Landau parameter from ${F}_{1}>\ensuremath{-}1$ in the superconducting phase to ${F}_{1}=\ensuremath{-}1$ in the pseudo-gap phase, corresponding to a state with spin-charge separation. The consequences of this proposal are discussed.
We study the two-dimensional spin-charge separated Ginzburg-Landau theory containing U(1) gauge interactions as a semi-phenomenological model describing fluctuating condensates in high temperature superconductivity. Transforming the original GL action, we abstract the effective action of Cooper pair. Especially, we clarify how Cooper pair correlation evolves in the normal state from the point of view of spin-charge separation. Furthermore, we point out how Cooper pair couples to gauge field in a gauge-invariant way, stressing the insensitivity of Cooper pair to infrared gauge field fluctuation.