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arXiv:cond-mat/9605115

Statistics of holons and spinons in the t-J model

Ikuo Ichinose, Tetsuo Matsui, Sakakibara, K.

Published May 19, 1996• 0 citations
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Abstract

We study the statistics of holons and spinons in the framework of the gauge theory. We start with the t-J model in the slave-boson formalism and use Chern-Simons gauge theory to study the statistics transmutation of quasiexcitations in the charge-spin separated phase.
DOI
10.48550/arxiv.cond-mat/9605115

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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{\mathit{T}}_{\mathrm{CD}}TCD​, the CD transition temperature, and calculate TCD{\mathit{T}}_{\mathrm{CD}}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.
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.
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.