Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Two Hubbard Bands: Weight Transfer in Optical and One-Particle Spectra

Henk J. Eskes, Andrzej M. Oleś

Published Aug 29, 1994• 84 citations
Publisher

Abstract

We identify local kinetic-energy contributions which are responsible for the rapid weight transfer from the high- to the low-energy scale observed upon doping in strongly correlated materials. Using strong-coupling perturbation theory for the Hubbard model we derive expressions for the weights of the upper and lower Hubbard bands separately and evaluate them explicitly in one dimension. The optical conductivity is found to be a direct probe of the local spin order.

DOI
10.1103/physrevlett.73.1279

Related papers

Spectral properties of the Hubbard bands

Henk J. Eskes, Andrzej M. Oleś, Marcel B. J. Meinders +1 more

Using strong-coupling perturbation theory for the Hubbard model, explicit expressions are obtained for the integrated weights, energy positions, and widths of the upper and lower Hubbard bands separately, both for the optical and photoemission spectrum. In one dimension all expressions can be explicitly evaluated using the large-U Bethe-ansatz wave function. The k\ensuremath{\rightarrow}-dependent moments for the one-particle spectrum are compared with the closely related two-pole ansatz. The strong momentum dependence of the spectra demonstrates the importance of the k\ensuremath{\rightarrow}-dependent correlation functions in the spectral moments, which are often neglected. In order to estimate corrections due to the neglect of higher-order terms (in t/U), all results are compared with numerical-diagonalization data for intermediate-U values. The sum-rule results show a rapid spectral-weight transfer from the high- to the low-energy regime upon doping, similar to what is observed experimentally in one-particle and optical spectra of Cu (high-${\mathit{T}}_{\mathit{c}}$) and Ni compounds. Such fast weight redistributions as a function of the carrier density are a natural consequence of the strong correlations in these materials. The redistribution of intensity in the optical conductivity is connected with the dilution of the spin system by the added holes. For the one-particle spectrum the decrease of weight in the upper Hubbard band away from half filling can be understood by state counting at U=\ensuremath{\infty}, and the effect is strongly enhanced for small doping by both the first- and second-order terms in t/U. Altogether, the one-particle and optical spectra show the importance of the three-site hopping term. Therefore the t-J model does not represent well the spectral properties of the Hubbard model at large U. The local spin order is essential and determines both the k\ensuremath{\rightarrow} dependence of the one-particle spectrum and the intensities in the optical spectrum.

Physical review. B, Condensed matter•Dec 15, 1994•158 citations

Nonlocal correlations in the optical conductivity spectra

D. A. Dobushovskyi, Andrij M. Shvaika

Optical conductivity spectra are studied for the Falicov-Kimball model with correlated hopping on the Bethe lattice.An expression for the current-current correlation function is derived using dynamical mean field theory.In the metallic phase with small correlated hopping values, the shape of Drude peak deviates from the Debye relaxation peak, and an additional wide peak is observed on the optical conductivity spectra and on Nyquist plot when Fermi level is in the vicinity of the two particle resonance.At larger values of the correlated hopping parameter, the density of states contains three bands and the corresponding optical spectra and Nyquist plots display a more complicated shape with additional peaks.For strong local correlations, the correlated hopping reduces the width of the upper Hubbard band resulting in a decrease of the Drude peak spectral weight for the doped Mott insulator.

arXiv:1806.10010•Condensed Matter Physics•Jun 1, 2018•3 citations

Optical conductivity of the Hubbard andt-Jmodels

Adriana Moreo, Elbio R. Dagotto

We calculate the optical conductivity \ensuremath{\sigma}(\ensuremath{\omega}) of the Hubbard and t-J models on 10- and 16-site lattices, respectively, using a Lanczos method. Results are presented for various values of the couplings U/t, J/t, and band fillings, using free- and periodic-boundary conditions. We discuss the behavior of the kinetic energy in the ground state, the distribution of spectral weight of \ensuremath{\sigma}(\ensuremath{\omega}) between low and high energies and the sum rule. Indications of a Drude-like peak at low energy in the one-hole subspace are observed in both models. Assuming that holes behave like independent (mass-renormalized) particles in the normal state of the superconductors, our results also suggest that the optical midinfrared broadband observed experimentally can be explained by hole excitations of strongly correlated systems.

Physical review. B, Condensed matter•Sep 1, 1990•100 citations

Dynamic Properties of Interacting Electrons.

L. Tan

The spectral weight functions and the optical conductivity of a highly correlated electronic system described by a simple Hubbard model are studied. The calculations are carried out for a small system, a cubic cluster of eight sites, by means of exact diagonalization using symmetrized basis functions. The spectral weight functions of a single hole (or electron) placed in an otherwise half-filled band are obtained. The density of states at different interaction strengths, ranging from weak to strong couplings, is studied. We observe the spreading of the spectral weight associated with some single-particle eigenstates over a large range of energies, and the appearance of satellite structure at higher excitation energies. The nature of band narrowing is also discussed. The frequency dependent (optical) conductivity is studied for the cases of a half-filled band, and for one hole and two hole dopings away from half filling. The interaction strength is varied between the weak- and strong-coupling limits. The formation of a Hubbard gap is observed. Results are related to aspects of the metal-insulator transition in bulk systems.

Civil War Book Review•Jan 1, 1993•0 citations

Emergence of quasiparticles in a doped Mott insulator

Yao Wang, Yu He, Krzysztof Wohlfeld +9 more

Abstract How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-Tc cuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La2−xSrxCuO4 (0 ≤ x ≤ 0.15). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-Tc cuprates.

arXiv:1909.09288•Communications Physics•Nov 13, 2020•17 citations

Spectral weight transfer in multiorbital Mott systems

Wei-Cheng Lee, Philip Phillips

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 $x=1/3$ to $x=1/(2{n}_{o}+1)$, where ${n}_{o}$ 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 $t$-$J$ 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 $x<[1/(2{n}_{o}+1)]$.

arXiv:1103.1637•Physical Review B•Sep 7, 2011•10 citations
We identify local kinetic-energy contributions which are responsible for the rapid weight transfer from the high- to the low-energy scale observed upon doping in strongly correlated materials. Using strong-coupling perturbation theory for the Hubbard model we derive expressions for the weights of the upper and lower Hubbard bands separately and evaluate them explicitly in one dimension. The optical conductivity is found to be a direct probe of the local spin order.
Using strong-coupling perturbation theory for the Hubbard model, explicit expressions are obtained for the integrated weights, energy positions, and widths of the upper and lower Hubbard bands separately, both for the optical and photoemission spectrum. In one dimension all expressions can be explicitly evaluated using the large-U Bethe-ansatz wave function. The k\ensuremath{\rightarrow}-dependent moments for the one-particle spectrum are compared with the closely related two-pole ansatz. The strong momentum dependence of the spectra demonstrates the importance of the k\ensuremath{\rightarrow}-dependent correlation functions in the spectral moments, which are often neglected. In order to estimate corrections due to the neglect of higher-order terms (in t/U), all results are compared with numerical-diagonalization data for intermediate-U values. The sum-rule results show a rapid spectral-weight transfer from the high- to the low-energy regime upon doping, similar to what is observed experimentally in one-particle and optical spectra of Cu (high-Tc{\mathit{T}}_{\mathit{c}}Tc​) and Ni compounds. Such fast weight redistributions as a function of the carrier density are a natural consequence of the strong correlations in these materials. The redistribution of intensity in the optical conductivity is connected with the dilution of the spin system by the added holes. For the one-particle spectrum the decrease of weight in the upper Hubbard band away from half filling can be understood by state counting at U=\ensuremath{\infty}, and the effect is strongly enhanced for small doping by both the first- and second-order terms in t/U. Altogether, the one-particle and optical spectra show the importance of the three-site hopping term. Therefore the t-J model does not represent well the spectral properties of the Hubbard model at large U. The local spin order is essential and determines both the k\ensuremath{\rightarrow} dependence of the one-particle spectrum and the intensities in the optical spectrum.
Optical conductivity spectra are studied for the Falicov-Kimball model with correlated hopping on the Bethe lattice.An expression for the current-current correlation function is derived using dynamical mean field theory.In the metallic phase with small correlated hopping values, the shape of Drude peak deviates from the Debye relaxation peak, and an additional wide peak is observed on the optical conductivity spectra and on Nyquist plot when Fermi level is in the vicinity of the two particle resonance.At larger values of the correlated hopping parameter, the density of states contains three bands and the corresponding optical spectra and Nyquist plots display a more complicated shape with additional peaks.For strong local correlations, the correlated hopping reduces the width of the upper Hubbard band resulting in a decrease of the Drude peak spectral weight for the doped Mott insulator.
We calculate the optical conductivity \ensuremath{\sigma}(\ensuremath{\omega}) of the Hubbard and t-J models on 10- and 16-site lattices, respectively, using a Lanczos method. Results are presented for various values of the couplings U/t, J/t, and band fillings, using free- and periodic-boundary conditions. We discuss the behavior of the kinetic energy in the ground state, the distribution of spectral weight of \ensuremath{\sigma}(\ensuremath{\omega}) between low and high energies and the sum rule. Indications of a Drude-like peak at low energy in the one-hole subspace are observed in both models. Assuming that holes behave like independent (mass-renormalized) particles in the normal state of the superconductors, our results also suggest that the optical midinfrared broadband observed experimentally can be explained by hole excitations of strongly correlated systems.
The spectral weight functions and the optical conductivity of a highly correlated electronic system described by a simple Hubbard model are studied. The calculations are carried out for a small system, a cubic cluster of eight sites, by means of exact diagonalization using symmetrized basis functions. The spectral weight functions of a single hole (or electron) placed in an otherwise half-filled band are obtained. The density of states at different interaction strengths, ranging from weak to strong couplings, is studied. We observe the spreading of the spectral weight associated with some single-particle eigenstates over a large range of energies, and the appearance of satellite structure at higher excitation energies. The nature of band narrowing is also discussed. The frequency dependent (optical) conductivity is studied for the cases of a half-filled band, and for one hole and two hole dopings away from half filling. The interaction strength is varied between the weak- and strong-coupling limits. The formation of a Hubbard gap is observed. Results are related to aspects of the metal-insulator transition in bulk systems.
Abstract How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-Tc cuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La2−xSrxCuO4 (0 ≤ x ≤ 0.15). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-Tc cuprates.
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)].