We construct a new U(1) slave-spin representation for the single-band Hubbard model in the large-U limit. The mean-field theory in this representation is more amenable to describe both the spin-charge-separation physics of the Mott insulator at half-filling and the strange metal behavior at finite doping. By employing a dynamical Green’s function theory for slave spins, we calculate the single-particle spectral function of electrons. The result is comparable to that in dynamical mean field theories. We then formulate a dynamical t/U expansion for the doped Hubbard model that reproduces the mean-field results at the lowest order of expansion. To the next order of expansion, it naturally yields an effective low-energy theory of a t–J model for spinons self-consistently coupled to an XXZ model for the slave spins. We show that the superexchange J is renormalized by doping, in agreement with the Gutzwiller approximation. Surprisingly, we find a new ferromagnetic channel of exchange interactions which survives in the infinite U limit, as a manifestation of the Nagaoka ferromagnetism.
We construct a new U(1) slave-spin representation for the single-band Hubbard model in the large-U limit. The mean-field theory in this representation is more amenable to describe both the spin-charge-separation physics of the Mott insulator at half-filling and the strange metal behavior at finite doping. By employing a dynamical Green’s function theory for slave spins, we calculate the single-particle spectral function of electrons. The result is comparable to that in dynamical mean field theories. We then formulate a dynamical t/U expansion for the doped Hubbard model that reproduces the mean-field results at the lowest order of expansion. To the next order of expansion, it naturally yields an effective low-energy theory of a t–J model for spinons self-consistently coupled to an XXZ model for the slave spins. We show that the superexchange J is renormalized by doping, in agreement with the Gutzwiller approximation. Surprisingly, we find a new ferromagnetic channel of exchange interactions which survives in the infinite U limit, as a manifestation of the Nagaoka ferromagnetism.
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 U 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 U 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 U limit, intersite Coulomb repulsion V strongly suppresses the single-particle weight of the metallic state.
The Mott metal-insulator transition in the Hubbard model is studied by constructing a dynamical slave-boson mean-field theory in the limit of large lattice coordination number z that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. On the Mott insulating side where all doublons and holons bond in real space into excitonic pairs leading to the charge gap, the theory simplifies considerably to leading order in 1/z and becomes exact on the infinite-z Bethe lattice. An asymptotic solution is obtained for a continuous Mott transition associated with the closing of the charge gap at a critical value of the Hubbard Uc and the corresponding doublon density ndc, hopping ${\ensuremath{\chi}}_{d}^{c}$ and doublon-holon pairing ${\mathrm{\ensuremath{\Delta}}}_{d}^{c}$ amplitudes. We find ${U}_{c}={U}_{\mathrm{BR}}[1\ensuremath{-}2{n}_{d}^{c}\ensuremath{-}\sqrt{z}({\ensuremath{\chi}}_{d}^{c}+{\mathrm{\ensuremath{\Delta}}}_{d}^{c})]\ensuremath{\simeq}0.8{U}_{\mathrm{BR}}$, where UBR is the critical value for the Brinkman-Rice transition in the Gutzwiller approximation captured in the static mean-field solution of the slave-boson formulation of Kotliar and Ruckenstein. Thus, the Mott transition can be viewed as the quantum correction to the Brinkman-Rice transition due to doublon-holon binding. Quantitative comparisons are made to the results of the dynamical mean-field theory, showing good agreement. In the absence of magnetic order, the Mott insulator is a U(1) quantum spin liquid with nonzero intersite spinon hopping that survives the large-z limit and lifts the 2N-fold degeneracy of the local moments. We show that the spinons are coupled to the doublons/holons by a dissipative compact U(1) gauge field in the deconfined phase, realizing the spin-charge separated gapless spin liquid Mott insulator.
Magnetic properties of Hubbard model have been studied extensively. A theoretical description of these states, however, is not straight forward within conventional mean-field approach due to the electron correlation effects. Here we provide a slave spin theory of the magnetic states in the single band Hubbard model. By introducing an additional decomposition of the on-site Coulomb interaction in the magnetic channel in both the slave spin and the fermionic spinon sectors, we show a magnetic solution with renormalized quasiparticle spectral weight can be stabilized at both half-filling and finite doping. By comparing the energies of antiferromagnetic and ferromagnetic states, we provide a ground-state phase diagram for generic electron filling. We further discuss possible generalization of the slave-spin method.
We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon–doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon–doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott–Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.
We reformulate the time-dependent Gutzwiller approximation by M. Schir\'o and M. Fabrizio, [Phys. Rev. Lett. 105, 076401 (2010)] in the framework of slave-boson mean-field theory, which is used to investigate the dynamical Mott transition of the generic two-band Hubbard model at half filling upon an interaction quench. Interorbital fluctuations lead to notable changes with respect to the single-band case. The singular dynamical transition is replaced by a broad regime of long-lived fluctuations between metallic and insulating states, accompanied by intriguing precursor behavior. A mapping to a spin model proves helpful to analyze the different regions in terms of the evolution of an Ising-like order parameter. Contrary to the static case, singlet occupations remain vital in the Mott-insulating regime with finite Hund's exchange.
We discuss the relevance of the improved mean-field slave-fermion theory to describe the Nagaoka $(U=\ensuremath{\infty})$ limit of the Hubbard model. In this theory the crucial on-site constraint of no double electron occupancy is taken into account rigorously prior to the mean-field approximation. At one-loop approximation the effective mean-field action shows a long-range ferromagnetic order over the whole doping range. This indicates that the slave-fermion mean-field theory does not constitute an appropriate framework to describe the physics of the Nagaoka phase. We discuss the drawbacks of this mean-field theory and present some results on the derivation of a low-energy effective spin action to describe the Nagaoka phase beyond the mean-field approximation.