Implication of our recent proposal [J. Phys. Soc. Jpn. 65 (1996) 687] to treat large-amplitude gauge-field fluctuations around the slave-boson mean-field theory for the t-J model has been explored in detail. By attaching gauge flux to spinons and holons and then treating them as free g-on's which respect the time-reversal symmetry, the optimum exclusion (g) and exchange (\a) statistics have been determined in the plane of doping rate and temperature. Two different relations between \a and g have been investigated, namely g=|\a| (Case1) and g=|\a|(2-|\a|) (Case2). The results indicate that slave fermion is favored at low doping while slave boson at high doping. For two dimension, in Case1 intermediate statistics are found in between, while in Case2 no intermediate statistics are found. The consequences of varying the dimensionality and strength of J have been studied also. The latter has no qualitative effect for both cases, while the former has a profound effect in Case1.
We analyze a class of mean-field flux phases of the slave boson t-J model, and present a finite-temperature phase diagram. The mean-field theory arises from a decomposition of the four-fermion terms into exchange, pairing, and direct terms, using Hubbard-Stratonovich fields. We find numerically that at low doping staggered flux phases are energetically favorable over the d-wave-pairing state. Very close to half filling a \ensuremath{\pi}-flux phase becomes stable. The occurrence of flux phases suppresses the pairing gap transition temperature.
The extended t - J model has been studied in the slave boson scheme. It is found that there exists some range of parameters where the chiral spin state is stabilized within a mean field approximation. The Chern-Simons Lagrangian for the gauge field, which represents the fluctuation of the phases of the order parameters and the local constraint, is obtained by integrating out spin fermion fields as in the undoped case [Wen, Wilczek and Zee: Phys. Rev. B 39 (1989) 11413]. The coefficient of this term turns out to depend on doping. Due to the coupling to this Chern-Simons gauge field, hole bosons are transmuted into anyons.
The extended t - J model, which has both transfer integral and exchange interaction between next-nearest neighbors besides those between nearest neighbors, has been investigated by the mean field approximation in the slave-boson scheme. Especially, the staggered flux state and the chiral spin state have been investigated. For the latter state, anyons are derived by use of the result of the Chern-Simons term for the doped case. It is shown that the prefactor of the Chern-Simons term and thus the fractional statistics depend on the degree of doping.
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 competition and possible coexistence of the flux phase and pairing states are considered within the slave-boson approach. In addition to the gauge field, coupling holons, and spinons, a statistical gauge field is introduced to account for the hard-core nature of holons. Using the equivalence of \ensuremath{\pi}-uniform and -staggered fluxes, we show the possibility of reducing the staggered flux and guaranteeing the commensurability condition of the uniform flux for holons at the same time. For certain dopings the frustration of the spinon gauge field to holon motion can be compensated by the holon's own statistical gauge field. Contrary to earlier conclusions of other authors, we find that the flux phase can coexist with the resonating-valence-bond (RVB) states below a critical doping concentration ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$, beyond which the d-wave RVB state takes over.
A slave-fermion gauge-theory approach of the t-J model: Doping-induced complex magnetic structure and Z
2 spin-gapped anomalous metal in an antiferromagnetic doped Mott insulator
We reinvestigate a doped antiferromagnetic Mott insulator based on the slave-fermion approach of the t-J model, where antiferromagnetic spin fluctuations and doped holes are described by bosonic spinons and fermionic holons, respectively. Earlier studies have shown that an effective field theory for the doped antiferromagnetic Mott insulator is given by a non-relativistic fermion (holon) U(1) gauge theory for charge dynamics and a relativistic boson (spinon) U(1) gauge theory for spin dynamics, thus allowing an anomalous metallic phase where bosonic spinons are gapped away from an antiferromagnetic state, analogous to the U(1) spin liquid phase in the slave-boson approach of the t-J model. We argue that the emergent U(1) gauge structure in this approach is based on a simplified picture for antiferromagnetic correlations. Considering that dynamics of doped holes frustrates a collinear antiferromagnetic spin configuration, we show that doped holes enhance ferromagnetic spin correlations and result in a complex magnetic structure. The presence of such a complex spin texture reduces the U(1) gauge structure down to Z
2, thus a different effective field theory results for the spin-gapped non-Fermi liquid metal at low temperatures because there are no gapless U(1) gauge fluctuations.