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arXiv:cond-mat/9508042 · Physical review. B, Condensed matter

Slave-particle quantization and sum rules in thet-Jmodel

J. C. Le Guillou, E. Ragoucy

Published Jul 15, 1995• 43 citations
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Abstract

In the framework of constrained systems, we give the classical Hamiltonian formulation of slave-particle models and their correct quantization. The electron-momentum distribution function in the t-J and Hubbard models is then studied in the framework of slave-particle approaches and within the decoupling scheme. We show that criticisms that have been addressed in this context coming from a violation of the sum rule for the physical electron are not valid. Due to the correct quantization rules for the slave particles, the sum rule for the physical electron is indeed obeyed, both exactly and within the decoupling scheme.

DOI
10.1103/physrevb.52.2403

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In the framework of constrained systems, we give the classical Hamiltonian formulation of slave-particle models and their correct quantization. The electron-momentum distribution function in the t-J and Hubbard models is then studied in the framework of slave-particle approaches and within the decoupling scheme. We show that criticisms that have been addressed in this context coming from a violation of the sum rule for the physical electron are not valid. Due to the correct quantization rules for the slave particles, the sum rule for the physical electron is indeed obeyed, both exactly and within the decoupling scheme.
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.
The quantization rules obtained by Le Guillou and Ragoucy in the slave particle theories of correlated systems have been applied to study the superconductivity in extended Hubbard and $t\ensuremath{-}J$ models. The quantization scheme has the virtue of treating the local constraint exactly. We compare our numerical results with those obtained in the mean-field approximation for usual slave boson technique. We also discuss the relation of the present approach with method of equation of motion for Hubbard operators. Where possible the obtained results are also compared with experimental data on high-temperature superconductors, as in these materials the essential physics is believed to depend on the presence of strong correlations.
We start from the Barnes-Coleman slave-particle description, where the Hubbard operators X are decomposed into a product of fermionic (fα) and bosonic (b) operators. The quantum mechanical constraint b † b+ ∑ α f † αfα = 1 is treated within the framework of Dirac’s method for the quantization of classical constrained systems. This leads to modified algebraic properties of the fundamental operators: bb † b = b, fαf † βfγ = δαβfγ and fαb † = 0. Thereby the algebra of the X-operators is preserved exactly on the operator level. Matrix representations of the above algebra are constructed and a resolvent-like perturbation theory for the single-impurity Anderson model is developed.
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​.
Using the mapping of the single-occupation space of the t-J model onto the tensor-product space of local spin-1/2 and holon states, the Hubbard operators and their products corresponding to physical quantities are expressed in terms of local spin and holon operators. All relevant operator relations of the t-J model are reproduced by this representation and no projection procedure is needed to remove the redundant degrees of freedom originating from the spin and charge decoupling. It is shown that the time-reversal symmetry requirement makes the essential restriction on the choice of the fictitious spin state associated with the electron-vacancy state in the mapping. The results are critically compared with the treatment of this topic in the paper of Wang and Rice [Phys. Rev. B 49, 4360 (1994)]. \textcopyright{} 1996 The American Physical Society.