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arXiv:cond-mat/0006500 · Journal of Physics A Mathematical and General

Fractionalization and confinement in theU(1) andZ2gauge theories of strongly correlated systems

T. Senthil, Matthew P. A. Fisher

Published Mar 2, 2001• 20 citations
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Abstract

Recently, we have elucidated the physics of electron fractionalization in strongly interacting electron systems using a Z 2 gauge theory formulation. Here we discuss the connection with the earlier U (1) gauge theory approaches based on the slave boson mean field theory. In particular, we identify the relationship between the holons and Spinons of the slave-boson theory and the true physical excitations of the fractionalized phases that are readily described in the Z 2 approach.

DOI
10.1088/0305-4470/34/10/106

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Recently, we have elucidated the physics of electron fractionalization in strongly interacting electron systems using a Z 2 gauge theory formulation. Here we discuss the connection with the earlier U (1) gauge theory approaches based on the slave boson mean field theory. In particular, we identify the relationship between the holons and Spinons of the slave-boson theory and the true physical excitations of the fractionalized phases that are readily described in the Z 2 approach.
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.
In a recent Letter, Nayak argued that slave partices are always confined in gauge theories of strongly-correlated electron systems like the t-J model. The argument mostly relies on Elitzur's theorem and the fact that the effective gauge theory under discussion is at infinite coupling. On the other hand, in the previous papers we studied dynamics of the gauge theory of the t-J model showing that the slave particles are in the Coulomb phase below certain critical temperature T{CSS} that depends on hole doping. We comment on the discrepancy between the results in two papers.
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