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Physical review. B, Condensed matter

Mechanism of charge-spin separation in thet-Jmodel: Dynamics ofU(1) gauge theory with multiple gauge fields

Ikuo Ichinose, Tetsuo Matsui

Published May 1, 1995• 38 citations
Publisher

Abstract

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

DOI
10.1103/physrevb.51.11860

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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.
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.{A}_{i}.Ai​. The charge-spin separation occurs below a certain temperature, TCSS,{T}_{\mathrm{CSS}},TCSS​, as a deconfinement phenomenon of the dynamics of Ai.{A}_{i}.Ai​. Below a certain temperature TSG(<TCSS),{T}_{\mathrm{SG}}(<{T}_{\mathrm{CSS}}),TSG​(<TCSS​), the spin-gap phase develops as the Higgs phase of the gauge-field dynamics, and Ai{A}_{i}Ai​ acquires a mass mA.{m}_{A}.mA​. The effective field theory near TSG{T}_{\mathrm{SG}}TSG​ takes the form of a Ginzburg-Landau theory of a complex scalar field $\ensuremath{\lambda}$ coupled with Ai,{A}_{i},Ai​, where $\ensuremath{\lambda}$ represents d-wave pairings of spinons. Three dimensionality of the system is crucial to realize a phase transition at TSG.{T}_{\mathrm{SG}}.TSG​. By using this field theory, we calculate the dc resistivity $\ensuremath{\rho}.$ At T>TSG,T>{T}_{\mathrm{SG}},T>TSG​, $\ensuremath{\rho}$ is proportional to T. At T<TSG,T<{T}_{\mathrm{SG}},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 1/21/21/2 and becomes a nonuniversal quantity which depends on temperature and doping. This significantly improves the comparison with the experimental data.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2{\mathit{T}}^{2}T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
In this paper we reexamine the problem of the separation of spin and charge degrees of freedom in two-dimensional strongly correlated systems. We establish a set of sufficient conditions for the occurrence of spin and charge separation. Specifically, we discuss this issue in the context of the Heisenberg model for spin-1/2 on a square lattice with nearest (J1{\mathit{J}}_{1}J1​) and next-nearest (J2{\mathit{J}}_{2}J2​) neighbor antiferromagnetic couplings. Our formulation makes explicit the existence of a local SU(2) gauge symmetry once the spin-1/2 operators are replaced by bound states of spinons. The mean-field theory for the spinons is solved numerically as a function of the ratio J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​ for the so-called s-RVB ansatz (s-RVB stands for short range resonating valence bond). A second-order phase transition exists in a flux state for J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​ larger than the critical value (J2/{\mathit{J}}_{2/}J2/​J1{\mathit{J}}_{1}J1​)cr{)}_{\mathrm{cr}})cr​ identify the range 0J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​(J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​)cr{)}_{\mathrm{cr}})cr​ as the s-RVB phase. It is characterized by the existence of a finite gap to the elementary excitations (spinons) and the breakdown of all the continuous gauge symmetries. An effective continuum theory for the spinons and the gauge degrees of freedom is constructed just below the onset of the flux phase. We argue that this effective theory is consistent with the deconfinement of the spinons carrying the fundamental charge of the gauge group. We contrast this result with the study of the one-dimensional quantum antiferromagnet within the same approach. We show that in the one-dimensional model, the spinons of the gauge picture are always confined and thus cannot be identified with the gapless spin-1/2 excitations of the quantum antiferromagnet Heisenberg model.
Fermionizing the charge sector and bosonizing the spin part in the SU(2) slave-boson theory, we derive an effective-field theory for dynamics of doped holes in the antiferromagnetically correlated spin background, where spin fluctuations are described by an SO(5) Wess-Zumino-Witten (WZW) theory while dynamics of doped holes is characterized by QED3{\text{QED}}_{3}QED3​ with a chemical-potential term. An important feature of our effective-field theory is the coupling term between valence-bond fluctuations and doped holes. Considering that valence-bond fluctuations are deeply related with monopole excitations of staggered U(1) gauge fields in the bosonic field theory for spin fluctuations, we demonstrate that hole dynamics helps deconfinement of bosonic spinons near the quantum critical point of the SO(5) WZW theory. We solve this effective-field theory in the Eliashberg framework and find non-Fermi-liquid physics in thermodynamics and transport, where z=3z=3z=3 criticality with dynamical exponent zzz plays an important role for hole dynamics. We discuss validity of our field theory, applying it to a doped spin chain and comparing it with the slave-fermion framework. Furthermore, we discuss instability of the anomalous metallic phase against superconductivity and density waves of doped holes, resulting from competition between gauge and valence-bond fluctuations.