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Physical review. B, Condensed matter

Lower and upper Hubbard bands: A slave-boson treatment

Roberto Raimondi, Claudio Castellani

Published Oct 15, 1993• 51 citations
Publisher

Abstract

We analyze the single-particle spectral density and the optical conductivity of the single-band Hubbard model in the insulating Mott phase within the slave-boson technique. We show that the boson fluctuations around the saddle-point solution build up the lower and upper Hubbard bands and give rise to the optical conductivity which describes transitions between these incoherent bands. We find that the Brinkman-Rice metal-insulator transition is characterized by the simultaneous vanishing of the jump in the chemical potential, the single-particle spectral density gap, and the optical gap.

DOI
10.1103/physrevb.48.11453

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We analyze the single-particle spectral density and the optical conductivity of the single-band Hubbard model in the insulating Mott phase within the slave-boson technique. We show that the boson fluctuations around the saddle-point solution build up the lower and upper Hubbard bands and give rise to the optical conductivity which describes transitions between these incoherent bands. We find that the Brinkman-Rice metal-insulator transition is characterized by the simultaneous vanishing of the jump in the chemical potential, the single-particle spectral density gap, and the optical gap.
We analyze the single-particle and collective excitations near the metal to charge-transfer insulator transition, using the slave-boson technique. We show that the Mott transition can be interpreted as a softening of an auxiliary Bose excitation. In the insulating phase the energy of the boson at zero momentum is related to the jump in the chemical potential at zero doping. The dispersion of the collective modes gives rise to the structure of the incoherent Hubbard bands. A similar picture holds for the single-band Hubbard model.
The conventional viewpoint of the strongly correlated electron metal-insulator transition is that a single band splits into two upper and lower Hubbard bands at the transition. Much work has investigated whether this transition is continuous or discontinuous. Here we focus on another aspect and ask the question of whether there are additional upper and lower Hubbard bands, which stretch all the way out to infinity — leading to an infinite single-particle bandwidth (or spectral range) for the Mott insulator. While we are not able to provide a rigorous proof of this result, we use exact diagonalization studies on small clusters to motivate the existence of these additional bands, and we discuss some different methods that might be utilized to provide such a proof. Even though the extra upper and lower Hubbard bands have very low total spectral weight, those states are expected to have extremely long lifetimes, leading to a nontrivial contribution to the transport density of states for [Formula: see text] transport and modifying the high temperature limit for the electrical resistivity.
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 zzz 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/z1/\sqrt{z}1/z​ and becomes exact on the infinite-zzz 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{U}_{c}Uc​ and the corresponding doublon density ndc{n}_{d}^{c}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{U}_{\mathrm{BR}}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)U(1)U(1) quantum spin liquid with nonzero intersite spinon hopping that survives the large-zzz limit and lifts the 2N{2}^{N}2N-fold degeneracy of the local moments. We show that the spinons are coupled to the doublons/holons by a dissipative compact U(1)U(1)U(1) gauge field in the deconfined phase, realizing the spin-charge separated gapless spin liquid Mott insulator.
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.
We investigate the ground state phase diagram of the one-dimensional ionic Hubbard model with an alternating potential at half-filling by the bosonization technique as well as by numerical diagonalization of finite systems with the Lanczos and DMRG methods. Our results support the existence of a single "metallic" transition point from a band to a correlated insulator with simultaneous charge and bond-charge order. In addition, we present results for the optical conductivity obtained by the dynamical DMRG method. The insulator-insulator phase transition scenario is discussed in detail including a critical review of existing approaches and results for the ionic Hubbard model.
We use the Kotliar-Ruckenstein slave-boson formalism to study the temperature dependence of paramagnetic phases of the one-band Hubbard model for a variety of band structures. We calculate the Fermi liquid quasiparticle spectral weight ZZZ and identify the temperature at which it decreases significantly to a crossover to a bad metal region. Near the Mott metal-insulator transition, this coherence temperature Tcoh{T}_{\mathrm{coh}}Tcoh​ is much lower than the Fermi temperature of the uncorrelated Fermi gas, as is observed in a broad range of strongly correlated electron materials. After a proper rescaling of temperature and interaction, we find a universal behavior that is independent of the band structure of the system. We obtain the temperature-interaction phase diagram as function of doping, and we compare the temperature dependence of the double occupancy, entropy, and charge compressibility with previous results obtained with dynamical mean-field theory. We analyze the stability of the method by calculating the charge compressibility.