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Journal of the Physical Society of Japan

Gauge Fields in Slave-Fermion Formalism. I. Destruction of the Néel Order

Kazuhiro Kuboki, D. Yoshioka

Published Feb 15, 1992• 4 citations
Publisher

Abstract

The t ′ - J model ( t ′ : transfer integral between next nearest neighbor sites) on a square lattice is studied within the slave-fermion formalism. In a mean-field approximation the antiferromagnetic long-range order (AFLRO), which is represented by the Bose condensation of the spinon at T =0, persists even for large doping rate. It is shown that the gauge field representing the fluctuations around the mean-field solution works in reducing the AFLRO, making the phase diagram of the ground state closer to that observed experimentally.

DOI
10.1143/jpsj.61.621

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The t ′ - J model ( t ′ : transfer integral between next nearest neighbor sites) on a square lattice is studied within the slave-fermion formalism. In a mean-field approximation the antiferromagnetic long-range order (AFLRO), which is represented by the Bose condensation of the spinon at T =0, persists even for large doping rate. It is shown that the gauge field representing the fluctuations around the mean-field solution works in reducing the AFLRO, making the phase diagram of the ground state closer to that observed experimentally.
A two-dimensional square-lattice Hubbard model is investigated. A slave-fermion formulation, in which the electron operator is expressed by a combination of bose operators for the spin freedom, and fermi operators for the charge freedom, is used. The phase diagram for the resonating valence bond (RVB) state is obtained. The RVB state shows long-range antiferromagnetic order at T =0, the period of which deviates from that of the commensurate Néel order as the system deviates from the half-filled case.
A mean-field treatment of the phase string effect in the $t\ensuremath{-}J$ model is presented. Such a theory is able to unite the antiferromagnetic (AF) phase at half-filling and the metallic phase at finite doping within a single theoretical framework. We find that the low-temperature occurrence of the AF long-range ordering (AFLRO) at half-filling and superconducting condensation in the metallic phase are all due to Bose condensations of spinons and holons, respectively, on the top of a spin background described by bosonic resonating-valence-bond pairing. The fact that both spinon and holon here are bosonic objects, as the result of the phase string effect, represents a crucial difference from the conventional slave-boson and slave-fermion approaches. This theory also allows an underdoped metallic regime where the Bose condensation of spinons can still exist. Even though the AFLRO is gone here, such a regime corresponds to a microscopic charge inhomogeneity with short-ranged spin ordering. We discuss some characteristic experimental consequences for those different metallic regimes. A perspective on broader issues based on the phase string theory is also discussed.
The Jordan–Wigner transformation is applied to the spatially anisotropic spin-1/2 Heisenberg model on a square lattice with the nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions. The transformed Hamiltonian describes the interacting spinless fermions that hop between neighbor sites in a gauge field. Using the mean-field-type approximation to both the direct interaction between fermions and the phase factors, which represent the gauge field, the problem is reduced to that concerning a free Fermi gas. Two types of antiferromagnetic ordering (the N´eel and collinear ones) are considered. By calculating the ground-state energies, the phase transitions induced by the interaction frustration were analyzed.
A slave-spin representation of fermion operators has recently been proposed for the half-filled single and multiband Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. We solve the resulting spin problem using the cluster mean-field approximation. This approximation takes short-range correlations into account by exact diagonalization on the cluster, whereas long-range correlations beyond the size of clusters are treated at the mean-field level. In the limit where the cluster has only one site and the interaction strength UUU is infinite, this approach reduces to the Gutzwiller approximation. There are some qualitative differences when the size of the cluster is finite. We first compute the critical UUU for the Mott transition as a function of a frustrating nearest-neighbor interaction on lattices relevant for various correlated systems, namely, the cobaltates, the layered organic superconductors and the high-temperature superconductors. For the triangular lattice, we also study the extended Hubbard model with nearest-neighbor repulsion. In addition to a uniform metallic state, we find a $\sqrt{(3)}\ifmmode\times\else\texttimes\fi{}\sqrt{(3)}$ charge density wave in a broad doping regime, including commensurate ones. We find that in the large UUU limit, intersite Coulomb repulsion VVV strongly suppresses the single-particle weight of the metallic state.
We introduce the generalization of the slave-spin mean-field method to broken-symmetry phases. Through a variational approach we derive the single-particle energy shift in the mean-field equations which generates the appropriate self-consistent field responsible for the stabilization of the broken symmetry. With this correction the different flavors of the slave-spin mean field are actually the same method and they give identical results to Kotliar-Ruckenstein slave bosons and to the Gutzwiller approximation. We apply our formalism to the N\'eel antiferromagnetic state and study it in multiorbital models as a function of the number of orbitals and Hund's coupling strength, providing phase diagrams in the interaction-doping plane. We show that the doped antiferromagnet in proximity of half filling is typically unstable toward insulator-metal and magnetic-nonmagnetic phase separation. Hund's coupling extends the range of this antiferromagnet, and favors its phase separation.
A slave-fermion gauge-theory approach of the t-J model: Doping-induced complex magnetic structure and Z2_{2}2​ spin-gapped anomalous metal in an antiferromagnetic doped Mott insulator
We reinvestigate a doped antiferromagnetic Mott insulator based on the slave-fermion approach of the t-J model, where antiferromagnetic spin fluctuations and doped holes are described by bosonic spinons and fermionic holons, respectively. Earlier studies have shown that an effective field theory for the doped antiferromagnetic Mott insulator is given by a non-relativistic fermion (holon) U(1) gauge theory for charge dynamics and a relativistic boson (spinon) U(1) gauge theory for spin dynamics, thus allowing an anomalous metallic phase where bosonic spinons are gapped away from an antiferromagnetic state, analogous to the U(1) spin liquid phase in the slave-boson approach of the t-J model. We argue that the emergent U(1) gauge structure in this approach is based on a simplified picture for antiferromagnetic correlations. Considering that dynamics of doped holes frustrates a collinear antiferromagnetic spin configuration, we show that doped holes enhance ferromagnetic spin correlations and result in a complex magnetic structure. The presence of such a complex spin texture reduces the U(1) gauge structure down to Z2_{2}2​, thus a different effective field theory results for the spin-gapped non-Fermi liquid metal at low temperatures because there are no gapless U(1) gauge fluctuations.