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Journal of Physics Condensed Matter

Spin-charge separation in strongly correlated electronic systems

Naoto Nagaosa

Published Dec 14, 1998• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/10/49/025

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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.
One of the central issues in the study of high-temperature superconducting cuprates which are composed of two-dimensional (2D) CuO 2 planes is whether the 2D systems with strong electron correlation behave as a Fermi liquid or a non-Fermi-liquid-like one-dimensional (1D) system with electron correlation. In this article, we start with the detailed examination of the electronic structure in cuprates and study theoretically the spin and charge dynamics in 1D and 2D cuprates. The theoretical background of spin-charge separation in the 1D model systems including the Hubbard and t - J models is presented. The first direct observation of collective modes of spin and charge excitations in a 1D cuprate, which are called spinons and holons respectively, in angle-resolved photoemission spectroscopy (ARPES) experiments is reviewed in the light of the theoretical results based on the numerically exact-diagonalization method. The charge and spin dynamics in 1D insulating cuprates is also discussed in connection with the spin-charge separation. The arguments are extended to the 2D cuprates, and the unique aspects of the electronic properties of high-temperature superconductors are discussed. Special emphasis is placed on the d-wave-like excitations in insulating 2D cuprates observed in ARPES experiments. We explain how the excitations are caused by the spin-charge separation. The charge stripes observed in the underdoped cuprates are examined in connection with spin-charge separation in real space.
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.
This review gives a rather general discussion of high temperature superconductors as an example of a strongly correlated material. The argument is made that in view of the many examples of unconventional superconductors discovered in the past twenty years, we should no longer be surprised that superconductivity emerges as a highly competitive ground state in systems where Coulomb repulsion plays a dominant role. The physics of the cuprates is discussed, emphasizing the unusual pseudogap phase in the underdoped region. It is argued that the resonating valence bond picture, as formulated using gauge theory with fermionic and bosonic matter fields, gives an adequate physical understanding, even though many details are beyond the powers of current calculational tools. The recent discovery of quantum oscillations in a high magnetic field is discussed in this context. Meanwhile, the problem of the quantum spin liquid (a spin system with antiferromagnetic coupling which refuses to order even at zero temperature) is a somewhat simpler version of the high T c problem where significant progress has been made recently. It is understood that the existence of matter fields can lead to deconfinement of the U (1) gauge theory in 2 + 1 dimensions, and novel new particles (called fractionalized particles), such as fermionic spinons which carry spin and no charge, and gapless gauge bosons can emerge to create a new critical state at low energies. We even have a couple of real materials where such a scenario may be realized experimentally. The paper ends with answers to questions such as: What limits T c if pairing is driven by an electronic energy scale? Why is the high T c problem hard? Why is there no consensus? And why is the high T c problem important?
The implications of angle-resolved photoemission spectroscopy on the issue of spin-charge separation are discussed from the viewpoint of slave-particle resonating-valence-bond theories. It is pointed out that the nonlocal phase string is essential to reproduce the two-peak structure experimentally observed in SrCuO2{}_{2}2​. The comparison between one-dimensional and two-dimensional cases is also made.
We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed Gossamer superconductivity. We apply a renormalized mean field theory to approximately take into account the strong correlation effect in partially projected Gutzwiller wave functions. At the half-filling, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion UUU from a Gossamer superconductor at small UUU. At the critical value U=UcU={U}_{c}U=Uc​, the charge carrier density and the superconducting (SC) order parameter change discontinuously from zero in the Mott insulating phase to finite values in the Gossamer SC phase. The first order transition is due to the interplay of the kinetic and spin exchange energies. As the electron density changes away from half-filling, the Gossamer SC state changes smoothly, while the Mott insulator is evolved into a resonating valence bond (RVB) SC state. The Gossamer and RVB SC states have the same pairing symmetry. The SC order parameter changes smoothly from a RVB SC state at U>UcU>{U}_{c}U>Uc​ to a Gossamer SC state at U<UcU<{U}_{c}U<Uc​ at a fixed nonhalf-filled electron density. We argue that the RVB SC state is smoothly connected to the Gossamer SC state, hence to the BCS state.