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Modern Physics Letters B

CHARGE-SPIN SEPARATION, FRACTIONAL STATISTICS AND SUPERCONDUCTIVITY IN THE t-J MODEL

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

Published Apr 10, 1993• 1 citation
Publisher

Abstract

A generalized slave-particle scheme is introduced to the t-J model including the non-local effects. We find a charge-spin decoupled state in which the non-local gauge fields play the roles of statistics-transmutation. As a result, the gauge fluctuation becomes massive and the electromagnetic response function exhibits the Meissner effect, like in the free-semion system, but without breaking the time-reversal and parity symmetries due to the cancellation between charge and spin degrees of freedom in the low-energy, long-wavelength regime. We also calculate the momentum distribution of electrons which shows a characteristic scale equals to the Fermi momentum kf.

DOI
10.1142/s0217984993000552

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Modern Physics Letters B•Jun 30, 1993•20 citations
A generalized slave-particle scheme is introduced to the t-J model including the non-local effects. We find a charge-spin decoupled state in which the non-local gauge fields play the roles of statistics-transmutation. As a result, the gauge fluctuation becomes massive and the electromagnetic response function exhibits the Meissner effect, like in the free-semion system, but without breaking the time-reversal and parity symmetries due to the cancellation between charge and spin degrees of freedom in the low-energy, long-wavelength regime. We also calculate the momentum distribution of electrons which shows a characteristic scale equals to the Fermi momentum kf.
A generalized slave-particle scheme is introduced to study the t-J model with nonlocal effects included. A charge-spin decoupled state is found in this scheme, in which the nonlocal gauge fields play a role of attaching fictitious quantized fluxes to the particles as an effective way to describe antiferromagnetic correlation. As a result, the gauge fluctuation is suppressed in the long-wavelength limit, which shows the stability of flux binding, and the electromagnetic response function of such a state exhibits the Meissner effect. An important consequence of the present approach is that the electron, as a combination of the charge and spin degrees of freedom, does not show time-reversal and parity-symmetry-broken behavior, in contrast to the usual anyon theory. This is consistent with experimental results. The robustness of this conclusion relies on the exactness of the constraint between the charge and spin degrees of freedom as well as the flux binding condition. We also calculate the momentum distribution of electrons, which shows a characteristic scale equal to the Fermi momentum kf{\mathit{k}}_{\mathit{f}}kf​.
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.
The electron-momentum distribution function in the t-J model is studied in the framework of the slave-particle approach. Within the decoupling scheme used in gauge-field and related theories, we treat formally phase and amplitude fluctuations as well as constraints without further approximations. Our result indicates that the electron Fermi surface observed in high-resolution angle-resolved photoemission and inverse-photoemission experiments cannot be explained within this framework, and the sum rule for the physical electron is not obeyed. A correct scaling behavior of the electron-momentum distribution function near k\ensuremath{\sim}kF{\mathit{k}}_{\mathit{F}}kF​ and k\ensuremath{\sim}3kF{\mathit{k}}_{\mathit{F}}kF​ in one dimension can be reproduced by considering the nonlocal string fields [Z. Y. Weng et al., Phys. Rev. B 45, 7850 (1992)], but the overall momentum distribution is still not correct, at least at the mean-field level.
A simple picture for decoupling the charge and spin degrees of freedom is proposed and used to discuss the properties of the ground-state wave function of the one-dimensional t-J model. In the limit of J/t << 1 or delta << 1 we show that the ground state of the t-J model is well approximated by a wave function where the charge and spin degrees of freedom are separated: the spin degree of freedom is described by a "squeezed" Heisenberg model, where all the vacant sites are omitted and the charge degrees of freedom are described by a spinless-fermion Hamiltonian with nearest-neighbor attractive interactions.
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.
We propose a new fermion-spin transformation to implement the charge-spin separation in the large U Hubbard, or the equivalent t-J model. The charge degree of freedom is represented by a spinless fermion while the spin degree of freedom is represented by a hard-core boson. The local constraint for single occupancy is exactly satisfied. Very good agreement with exact solution is obtained for one-dimensional case in the mean field approximation, regarding the total energy, gapless spinon and holon spectra, and the momentum distribution of physical electrons. The same approximation yields good doping dependence of the staggered magnetization in the two-dimensional case.