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arXiv:cond-mat/9502113 · Physical review. B, Condensed matter

Spin-charge separation in thet-Jmodel: Magnetic and transport anomalies

Zheng-Yu Weng, D. N. Sheng, C. S. Ting

Published Jul 1, 1995• 35 citations
arXivHTMLPDF

Abstract

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 ${\mathit{T}}^{2}$ Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-${\mathit{T}}_{\mathit{c}}$ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.

DOI
10.1103/physrevb.52.637

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The spin-charge separation (SCS) in 1D and 2D are discussed from the viewpoint of gauge theory. For 1D I discuss the angle-resolved photoemission spectra (ARPES), which show clear evidence for the spin-charge separation. For 2D the underdoped cuprates are discussed, where the three classes of electronic state, i.e., the Néel state (N), the valence-bond solid (VBS) state and the resonating-valence-bond (RVB) state, are relevant. These states can be understood in terms of the competition between (i) magnetic ordering versus singlet formation and (ii) confinement versus deconfinement of the gauge field. It is fairly easy to understand the former, (i), but the latter, (ii), is more subtle and has not yet been established. I argue that the deconfining phase, i.e., the RVB state, is a new state of matter with SCS, and is realized when the sheet resistance is less than a critical value of the order of the quantum resistance . This condition is equivalent to that for superconductivity in the Josephson network model. The anomalous Kondo effect due to the non-magnetic impurities doped into the system reflects the non-Fermi-liquid nature of the host electronic state, and hence is the most promising experimental evidence for this new state of matter. We put special emphasis on the residual resistivity, and propose that its value provides a clear test for SCS.

Journal of Physics Condensed Matter•Dec 14, 1998•2 citations
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.
We propose an explanation of several experimental features related to the "pseudogap" in high Tc cuprates in terms of a spin-charge gauge theory. In this approach, based on a formal spin-charge separation applied to the t-J model, the low energy effective action describes gapful spinons (with a theoretically derived doping dependence of the gap ms~J(δ| ln δ|)1/2, where δ is the doping concentration) and holons with "small" Fermi surface (∊F~tδ) interacting via a gauge field. The main effect of gauge fluctuations is to introduce a dissipation ~T/χ, where χ is the diamagnetic susceptibility. The competition between the two energy scales, ms and T/χ, is the root in our approach of many phenomena peculiar to in-plane transport properties of the "pseudogap phase". Furthermore the gauge interaction induces binding of spinon and holon into an "electron" resonance. This binding introduces another energy scale, the recombination rate, which dominates the out-of-plane resistivity, yielding an insulating behavior. A good agreement is found between the experimental data and theoretically derived doping and temperature dependence of resistivity, both in-plane and out-of-plane, and spin relaxation.
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 fermion-spin transformation is used to implement the charge-spin separation, and is developed to study the low-dimensional t-J model. In this approach, the charge and spin degrees of freedom of the physical electron are separated, and the charge degree of freedom is represented by a spinless fermion while the spin degree of freedom is representd by a hard-core boson. The on-site local constraint for single occupancy is satisfied even in the mean-field approximation and the sum rule for the physical electron is obeyed. This approach can be applied to both one and two-dimensional systems. In the one-dimensional case, the spinon as well as the physical electron behave like Luttinger liquids. We have obtained a gapless charge and spin excitation spectrum, a good ground state energy, and a reasonable electron-momentum distribution within the mean-field approximation. The correct exponents of the correlation functions and momentum distribution are also obtained if the squeezing effect and rearrangement of the spin configurations are taken into account. In the two-dimensional case, within the mean-field approximation the magnetized flux state with a gap in the spinon spectrum has the lowest energy at half filling. The antiferromagnetic long-range order is destroyed by hole doping of the order \ensuremath{\sim}10-15 % for t/J=3-5 and a disordered flux state with gapless spinon spectrum becomes stable. The calculated specific heat is roughly consistent with observed results on copper oxide superconductors. The possible phase separation is also discussed at the mean-field level.
Quasiparticle properties are explored in an effective theory of the $t\ensuremath{-}J$ model which includes two important components: spin-charge separation and unrenormalizable phase shift. We show that the phase shift effect indeed causes the system to be a non-Fermi liquid as conjectured by Anderson on general grounds. But this phase shift also drastically changes a conventional perception of quasiparticles in a spin-charge separation state: an injected hole will remain stable due to the confinement of spinon and holon by the phase shift field despite the background is a spinon-holon sea. True deconfinement only happens in the zero-doping limit where a bare hole will lose its integrity and decay into holon and spinon elementary excitations. The Fermi-surface structure is completely different in these two cases, from a large band-structure-like one to four Fermi points in one-hole case, and we argue that the so-called underdoped regime actually corresponds to a situation in between, where the ``gaplike'' effect is amplified further by a microscopic phase separation at low temperature. Unique properties of the single-electron propagator in both normal and superconducting states are studied by using the equation of motion method. We also comment on some influential ideas proposed in the literature related to the Mott-Hubbard insulator and offer a unified view based on the present consistent theory.
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.
The spin-charge separation (SCS) in 1D and 2D are discussed from the viewpoint of gauge theory. For 1D I discuss the angle-resolved photoemission spectra (ARPES), which show clear evidence for the spin-charge separation. For 2D the underdoped cuprates are discussed, where the three classes of electronic state, i.e., the Néel state (N), the valence-bond solid (VBS) state and the resonating-valence-bond (RVB) state, are relevant. These states can be understood in terms of the competition between (i) magnetic ordering versus singlet formation and (ii) confinement versus deconfinement of the gauge field. It is fairly easy to understand the former, (i), but the latter, (ii), is more subtle and has not yet been established. I argue that the deconfining phase, i.e., the RVB state, is a new state of matter with SCS, and is realized when the sheet resistance is less than a critical value of the order of the quantum resistance . This condition is equivalent to that for superconductivity in the Josephson network model. The anomalous Kondo effect due to the non-magnetic impurities doped into the system reflects the non-Fermi-liquid nature of the host electronic state, and hence is the most promising experimental evidence for this new state of matter. We put special emphasis on the residual resistivity, and propose that its value provides a clear test for SCS.