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Physical review. B, Condensed matter

Spectral-weight transfer: Breakdown of low-energy-scale sum rules in correlated systems

M.B.J. Meinders, Henk J. Eskes, G. A. Sawatzky

Published Aug 1, 1993• 221 citations
Publisher

Abstract

In this paper we study the spectral-weight transfer from the high- to the low-energy scale by means of exact diagonalization of finite clusters for the Mott-Hubbard and charge-transfer model. We find that the spectral-weight transfer is very sensitive to the hybridization strength as well as to the amount of doping. This implies that the effective number of low-energy degrees of freedom is a function of the hybridization and therefore of the volume and temperature. In this sense it is not possible to define a Hamiltonian which describes the low-energy-scale physics unless one accepts an effective nonparticle conservation.

DOI
10.1103/physrevb.48.3916

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In this paper we study the spectral-weight transfer from the high- to the low-energy scale by means of exact diagonalization of finite clusters for the Mott-Hubbard and charge-transfer model. We find that the spectral-weight transfer is very sensitive to the hybridization strength as well as to the amount of doping. This implies that the effective number of low-energy degrees of freedom is a function of the hybridization and therefore of the volume and temperature. In this sense it is not possible to define a Hamiltonian which describes the low-energy-scale physics unless one accepts an effective nonparticle conservation.
A qualitative and quantitative description (exact diagonalization of finite clusters) of the doping dependence of one-electron-removal and -addition spectral weights is given. A half-filled Hubbard system in the localized limit has two low-energy electron-addition (removal) states for each hole (electron) created by doping. In contrast, a charge-transfer system in the localized limit is fundamentally asymmetric between hole and electron doping. However, when the hybridization is increased this asymmetry disappears quickly and both holes and electrons introduced by doping show a strongly correlated behavior.
The low-energy physics of the Emery model, representing the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates, can be understood by separating intracell interference within CuO4{\mathrm{CuO}}_{4}CuO4​ cells from intercell correlations described by an effective single-band Hubbard model. This decomposition explains the anomalous transfer of spectral intensity from the high- to the low-energy scale, the asymmetry between electron and hole doping, and the breakdown of low-energy sum rules. These features are related to the existence of an antibound charge transfer exciton band, are are very sensitive to the strength of the Coulomb repulsion Ud{\mathit{U}}_{\mathit{d}}Ud​.
We develop here a general formalism for multiorbital Mott systems that can be used to understand dynamical and static spectral weight transfer. We find that the spectral weight transferred from the high-energy scales is greatly increased as a result of the multiorbital structure. As a consequence certainly dynamically generated symmetries are obtained at lower values of doping than in the single-band Hubbard model. For example, in the atomic limit for filling less than one electron per site, the particle-hole symmetric condition in the lower band shifts from the one-band result of x=1/3x=1/3x=1/3 to x=1/(2no+1)x=1/(2{n}_{o}+1)x=1/(2no​+1), where no{n}_{o}no​ is the number of orbitals with an unpaired spin. Transport properties computed from effective low-energy theories that forbid double occupancy of bare electrons, such as the multiorbital ttt-JJJ generalization, should all be be sensitive to this particle-hole symmetric condition. Away from the atomic limit, the dynamical contributions increase the transferred spectral weight. Consequently, any phenomena that are sensitive to an emergent particle-hole symmetry should be obtained at x<[1/(2no+1)]x<[1/(2{n}_{o}+1)]x<[1/(2no​+1)].
We show that doped Mott insulators exhibit a collective degree of freedom, not made out of the elemental excitations, because the number of single-particle addition states at low energy per electron per spin is greater than one. The presence of such a collective degree of freedom which is not a consequence of proximity to a phase transition is a consequence of dynamical spectral weight transfer from high to low energies. This physics is captured by the charge 2e2e2e boson that emerges by explicitly integrating out the high-energy scale in the Hubbard model. The charge 2e2e2e boson binds to a hole, thereby mediating new charge eee states at low energy. It is the presence of such charge eee states which have no counterpart in the non-interacting system that provides the general mechanism for the breakdown of Fermi liquid theory in doped Mott insulators. The relationship between the charge 2e2e2e boson formulation and the standard perturbative treatment is explained.
The shift in the spectral weight distribution under doping is termed the spectral weight transfer (SWT) and is a key indicator of strongly correlated physics. The static SWT (t=0t=0t=0) for doping fraction xxx scales as xxx for semiconductors and as 2x2x2x for Mott insulators. The SWT receives corrections in t/Ut/Ut/U due to the noncommutativity of the kinetic and interaction terms in the Hamiltonian, termed the dynamic SWT. We compute explicitly the low-energy spectral weight (LESW) in the lower Hubbard band using the orbital Hatsugai-Kohmoto (OHK) model. We show that the dynamical mixing enters the LESW with a universal slope independent of the number of orbitals. This independence on orbital number corroborates the rapid convergence of the OHK model to the Hubbard model. As a result, OHK is an effective simulator of Hubbard physics.
We study the spectral weight transfer and the chemical potential shift in strongly correlated electron systems caused by carrier doping by applying the dynamical mean-field theory to a two-band Hubbard model. The parameters of the model are chosen so that the undoped system is a charge-transfer-type insulator. We find that in the insulating phase there are finite intensities corresponding to local singlet states formed by hybridized d and p electrons, and that, on doping a part of them, turn into itinerant states. The results are discussed in the light of experimental and theoretical results for high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates. \textcopyright{} 1996 The American Physical Society.