The multiorbital Hubbard model is expressed in terms of quantum phase variables (``slave rotors'') conjugate to the local charge, and of auxiliary fermions, providing an economical representation of the Hilbert space of strongly correlated systems. When the phase variables are treated in a local mean-field manner, similar results to the dynamical mean-field theory are obtained, namely a Brinkman-Rice transition at commensurate fillings together with a ``preformed'' Mott gap in the single-particle density of states. The slave-rotor formalism allows to go beyond the local description and take into account spatial correlations, following an analogy to the superfluid-insulator transition of bosonic systems. We find that the divergence of the effective mass at the metal-insulator transition is suppressed by short range magnetic correlations in finite-dimensional systems. Furthermore, the strict separation of energy scales between the Fermi-liquid coherence scale and the Mott gap, found in the local picture, holds only approximately in finite dimensions, due to the existence of low-energy collective modes related to zero-sound.
The multiorbital Hubbard model is expressed in terms of quantum phase variables (slave rotors'') conjugate to the local charge, and of auxiliary fermions, providing an economical representation of the Hilbert space of strongly correlated systems. When the phase variables are treated in a local mean-field manner, similar results to the dynamical mean-field theory are obtained, namely a Brinkman-Rice transition at commensurate fillings together with a preformed'' Mott gap in the single-particle density of states. The slave-rotor formalism allows to go beyond the local description and take into account spatial correlations, following an analogy to the superfluid-insulator transition of bosonic systems. We find that the divergence of the effective mass at the metal-insulator transition is suppressed by short range magnetic correlations in finite-dimensional systems. Furthermore, the strict separation of energy scales between the Fermi-liquid coherence scale and the Mott gap, found in the local picture, holds only approximately in finite dimensions, due to the existence of low-energy collective modes related to zero-sound.
We review a representation of Hubbard-like models that is based on auxiliary pseudospin variables. These pseudospins refer to the local charge modulo two in the original model and display a local Z2 gauge freedom. We discuss the associated mean-field theory in a variety of different contexts which are related to the problem of the interaction-driven metal-insulator transition at half-filling including Fermi surface deformation and spectral features beyond the local approximation. Notably, on the mean-field level, the Hubbard bands are derived from the excitations of an Ising model in a transverse field and the quantum critical point of this model is identified with the Brinkman-Rice criticality of the almost localized Fermi liquid state. Nonlocal correlations are included using a cluster mean-field approximation and the Schwinger boson theory for the auxiliary quantum Ising model.
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.
A new mean field theory is proposed for the Mott transition in the Hubbard model based on the slave rotor representation of the electron operator. This theory provides a better description of the role of the long range charge correlation in the Mott insulating state and offers a good estimation of the critical correlation strength for the Mott transition. We have constructed a new variational wave function for the Mott insulating state based on this new slave rotor mean field theory. We find this new variational wave function outperforms the conventional Jastrow type wave function with long range charge correlator in the Mott insulating state. It predicts a continuous Mott transition with non-divergent quasiparticle mass at the transition point. We also show that the commonly used on-site mean field decoupling for the slave rotor corresponds to the Gutzwiller approximation for the Gutzwiller projected wave function with only on-site charge correlator, which can not describe the Mott transition in any finite dimensional system.
The Mott-Hubbard transition is a paradigmatic phenomenon driven by strong electronic correlations. We investigate this transition in a three-orbital modified periodic Anderson model using slave-rotor mean-field theory. A minimal two-site cluster extension is introduced to understand the minimal effects of short-range spatial correlations. In comparison to the single-site solution, short-range spatial correlations reveal a shift of the transition point. Going beyond the slave-rotor analysis, we also evaluate the dynamical self-energy and map it onto the boundary Green's function of a non-interacting semi-infinite auxiliary chain. For the metallic phase, the resulting hopping pattern corresponds to a topologically trivial generalized Su--Schrieffer--Heeger chain. This construction provides a framework for exploring the possible topological character of the Mott transition in this model.
In this short communication we discuss results obtained for the single and multi-orbital Hubbard models within the mean-field-slave-boson description of correlated fermions on a square lattice. For appropriate parameter values the results can be used to mimic some of the normal state properties of the copper oxide systems. Results for the single and multi-orbital models differ in a very characteristic manner. In the single band case the phase diagram consists of metallic (U<Uc) and strongly correlated (U>Uc) regions, which are clearly seperated at half filling (Uc being the critical value of the Brinkman-Rice transition1)). Upon doping the transition between these two phases smoothes out and for large enough doping (δ>0.2, δ=1−n) the system behaves as a weakly correlated metal. In the multi-oibital case depending on the input energies for the orbitals the transition to the insulating state can be either of the Brinkman-Rice or the charge-transfer type. Similar to the single band case doping causes rapid loss of correlation effects. We tentatively conclude that the Kondo-type of effect is absent in the multi-orbital model.