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

arXiv:cond-mat/0501029 · Physical Review B

Magnon and hole excitations in the two-dimensional half-filled Hubbard model

Weihong Zheng, Rajiv R. P. Singh, J. Oitmaa, Oleg P. Sushkov, Chris J. Hamer

Published Jul 18, 2005• 7 citations
arXivHTMLPDF

Abstract

Spin and hole excitation spectra and spectral weights are calculated for the half-filled Hubbard model, as functions of $t∕U$. We find that the high energy spin spectra are sensitive to charge fluctuations. The energy difference $\ensuremath{\Delta}(\ensuremath{\pi},0)\ensuremath{-}\ensuremath{\Delta}(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ in the single-magnon dispersion relation, which is negative for the Heisenberg model, changes sign at a fairly small $t∕U\ensuremath{\approx}0.053(5)$. The hole bandwidth is proportional to $J$, and considerably larger than in the $t\text{\ensuremath{-}}J$ models. It has a minimum at $(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ and a very weak dispersion along the antiferromagnetic zone boundary. A good fit to the measured spin spectra in ${\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$ at $T=10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is obtained with the parameter values $U=3.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, $t=0.35\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$.

DOI
10.1103/physrevb.72.033107

Related papers

Low-energy theory of the t−t′−t″−U Hubbard model at half-filling: Interaction strengths in cuprate superconductors and an effective spin-only description of La2CuO4

Jean-Yves P. Delannoy, Michel J. P. Gingras, P. C. W. Holdsworth +1 more

Spin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many other types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band-structure calculations and photoemission experiments on these systems, we include second- and third-neighbor hopping parameters, ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, into the Hubbard Hamiltonian. A unitary transformation method is used to find systematically the effective Hamiltonian and any operator in the spin-only representation. The results include all closed four-hop electronic pathways in the canonical transformation. The method generates many ring exchange terms that play an important role in the comparison with experiments on ${\text{La}}_{2}{\text{CuO}}_{4}$. Performing a spin-wave analysis, we calculate the magnon dispersion as a function of $U$, $t$, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$. The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. [Phys. Rev. Lett. 86, 5377 (2001)] for ${\text{La}}_{2}{\text{CuO}}_{4}$. The ring exchange terms are found essential, in particular to determine the relative sign of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, with the values found in good agreement with independent theoretical and experimental estimates for other members of the cuprate family. The zero-temperature sublattice magnetization is calculated using these parameters and also found to be in good agreement with the experimental value estimated by Lee et al. [Phys. Rev. B 60, 3643 (1999)]. We find a value of the interaction strength $U\ensuremath{\simeq}8t$ consistent with Mott insulating behavior.

arXiv:0808.3167•Physical Review B•Jun 24, 2009•57 citations

Linearized antiferromagnetic spin-wave spectra around a hole in the two-dimensional Hubbard model

Han-Yong Choi

We study the effects of doping on the spin fluctuations of the two-dimensional Hubbard model. Within a harmonic approximation we calculate the linearized antiferromagnetic spin-wave spectra around a hole away from half-filling, which takes the form of a spin polaron in a mean-field approximation. The presence of the spin polaron breaks a symmetry of the problem, the product of time reversal and lattice translation. As a result, the double degeneracy of the magnon spectra of the N\'eel state is lifted. There also appear localized magnon modes depending on the ratio U/t of the Hubbard model. The quantum correction due to the spin fluctuations is found to increase the spin polaron binding energy for U/t13, but decreases it for U/t>13.

Physical review. B, Condensed matter•Aug 1, 1991•7 citations

One- and two-hole excitation spectra of the Hubbard model in the non-half-filled case

Andrzej M. Oleś, Guy Tréglia, D. Spanjaard +1 more

Exact results for the one- and two-hole excitation spectra of the one- dimensional Hubbard model for filling larger than one electron per site are presented. We consider short chains of up to eight atoms and use the so-called modified periodic boundary conditions, with which we are able to extrapolate the results up to infinite chains. The one-hole excitation spectra demonstrate a gradual transition from the band picture to the spectra characterized by new satellite structures, with increasing electron-electron interaction U. The weight of the satellite part of these spectra increases with increasing U, approaching the atomic-limit value. In the ferromagnetic case, a substantial reduction of the exchange splitting is found as compared with the independent-electron approximation. The two-hole excitation spectra exhibit characteristic atomic lines at large values of U, while at intermediate values of U they are much broader in the non-completely-filled chain than the respective ones of the filled chain. The distance between the satellite and the band part is found to be larger than the value of U for small and intermediate values of the interaction. The results obtained support those found with second-order perturbation theory and the t-matrix approximation.

Physical review. B, Condensed matter•Oct 15, 1986•17 citations

Spectral function of holes in the Emery model

Patrick Unger, Peter Fulde

We calculate the single-particle excitation spectrum of holes in the Emery model thereby extending and improving previous calculations. The system is considered at half filling (${\mathit{n}}_{\mathit{h}}$=1, one hole per ${\mathrm{CuO}}_{2}$ unit) and for hole doping, where the on-site hole-hole repulsions are kept finite. A paramagnetic form of the ground state is used. For the determination of the retarded Green's functions of copper and oxygen holes, the projection technique is applied solving the resulting equations of motions self-consistently. At half filling, the excitation spectrum exhibits a charge-transfer gap bounded by Zhang-Rice singlet states and the upper Hubbard band. Upon hole doping the flat singlet band crosses the Fermi level giving rise to a large Fermi surface at a hole concentration of ${\mathit{n}}_{\mathit{h}}$=1.25. Moreover, spectral weight is shifted from the upper Hubbard band to the states near the Fermi energy. The calculated spectral densities, the singlet dispersion for the doped system, and the transfer of spectral weight are in good quantitative agreement with exact diagonalization results for 2\ifmmode\times\else\texttimes\fi{}2 ${\mathrm{CuO}}_{2}$ cluster.

Physical review. B, Condensed matter•Dec 1, 1993•49 citations

Systematic 1/Sstudy of the two-dimensional Hubbard model at half-filling

Andrey V. Chubukov, Karen A. Musaelian

The two-dimensional Hubbard model is extended by placing 2S orbitals at each lattice site and studied in a systematic 1/S expansion. The 1/S results for the magnetic susceptibility and the spectra of spin-wave excitations at half-filling are consistent with the large S calculations for the Heisenberg antiferromagnet. The 1/S corrections to the fermionic spectrum lift the degeneracy along the edge of the magnetic Brillouin zone yielding minima at (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2). Relation to previous papers on the subject is discussed.

arXiv:cond-mat/9402097•Physical review. B, Condensed matter•Sep 1, 1994•17 citations

One-hole excitation spectra of the one-dimensional Hubbard model

Andrzej M. Oleś, Guy Tréglia, D. Spanjaard +1 more

Exact results for the one-hole excitation spectra of the one-dimensional half-filled Hubbard Hamiltonian are presented. We consider short chains of N=2, 4, 6 atoms and introduce modified periodic boundary conditions which allow us to make a comparison between different N and to extrapolate the results up to infinite chains. By the increasing weight of the scattering states in the one-hole spectrum, we demonstrate a gradual disappearance of the free-electron (band) picture with increasing local electron-electron interaction U. The exact spectra of the N=6 chain verify the results of second-order perturbation theory for U/W1, where W is the bandwidth. The extrapolation to the infinite system, made with the finite-cell-scaling method, gives the gap which agrees rather well with the exact result for U/W>0.2. The average energies and weights of the band and scattering states obtained with this method for an infinite chain do not differ significantly from those of the N=6 chain.

Physical review. B, Condensed matter•Aug 15, 1985•15 citations
Spin and hole excitation spectra and spectral weights are calculated for the half-filled Hubbard model, as functions of t∕Ut∕Ut∕U. We find that the high energy spin spectra are sensitive to charge fluctuations. The energy difference \ensuremathΔ(\ensuremathπ,0)\ensuremath−\ensuremathΔ(\ensuremathπ∕2,\ensuremathπ∕2)\ensuremath{\Delta}(\ensuremath{\pi},0)\ensuremath{-}\ensuremath{\Delta}(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)\ensuremathΔ(\ensuremathπ,0)\ensuremath−\ensuremathΔ(\ensuremathπ∕2,\ensuremathπ∕2) in the single-magnon dispersion relation, which is negative for the Heisenberg model, changes sign at a fairly small t∕U\ensuremath≈0.053(5)t∕U\ensuremath{\approx}0.053(5)t∕U\ensuremath≈0.053(5). The hole bandwidth is proportional to JJJ, and considerably larger than in the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J models. It has a minimum at (\ensuremathπ∕2,\ensuremathπ∕2)(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)(\ensuremathπ∕2,\ensuremathπ∕2) and a very weak dispersion along the antiferromagnetic zone boundary. A good fit to the measured spin spectra in La2CuO4{\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}La2​CuO4​ at T=10KT=10\phantom{\rule{0.3em}{0ex}}\mathrm{K}T=10K is obtained with the parameter values U=3.1eVU=3.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}U=3.1eV, t=0.35eVt=0.35\phantom{\rule{0.3em}{0ex}}\mathrm{eV}t=0.35eV.
Spin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many other types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band-structure calculations and photoemission experiments on these systems, we include second- and third-neighbor hopping parameters, ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, into the Hubbard Hamiltonian. A unitary transformation method is used to find systematically the effective Hamiltonian and any operator in the spin-only representation. The results include all closed four-hop electronic pathways in the canonical transformation. The method generates many ring exchange terms that play an important role in the comparison with experiments on La2CuO4{\text{La}}_{2}{\text{CuO}}_{4}La2​CuO4​. Performing a spin-wave analysis, we calculate the magnon dispersion as a function of UUU, ttt, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$. The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. [Phys. Rev. Lett. 86, 5377 (2001)] for La2CuO4{\text{La}}_{2}{\text{CuO}}_{4}La2​CuO4​. The ring exchange terms are found essential, in particular to determine the relative sign of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, with the values found in good agreement with independent theoretical and experimental estimates for other members of the cuprate family. The zero-temperature sublattice magnetization is calculated using these parameters and also found to be in good agreement with the experimental value estimated by Lee et al. [Phys. Rev. B 60, 3643 (1999)]. We find a value of the interaction strength $U\ensuremath{\simeq}8t$ consistent with Mott insulating behavior.
We study the effects of doping on the spin fluctuations of the two-dimensional Hubbard model. Within a harmonic approximation we calculate the linearized antiferromagnetic spin-wave spectra around a hole away from half-filling, which takes the form of a spin polaron in a mean-field approximation. The presence of the spin polaron breaks a symmetry of the problem, the product of time reversal and lattice translation. As a result, the double degeneracy of the magnon spectra of the N\'eel state is lifted. There also appear localized magnon modes depending on the ratio U/t of the Hubbard model. The quantum correction due to the spin fluctuations is found to increase the spin polaron binding energy for U/t13, but decreases it for U/t>13.
Exact results for the one- and two-hole excitation spectra of the one- dimensional Hubbard model for filling larger than one electron per site are presented. We consider short chains of up to eight atoms and use the so-called modified periodic boundary conditions, with which we are able to extrapolate the results up to infinite chains. The one-hole excitation spectra demonstrate a gradual transition from the band picture to the spectra characterized by new satellite structures, with increasing electron-electron interaction U. The weight of the satellite part of these spectra increases with increasing U, approaching the atomic-limit value. In the ferromagnetic case, a substantial reduction of the exchange splitting is found as compared with the independent-electron approximation. The two-hole excitation spectra exhibit characteristic atomic lines at large values of U, while at intermediate values of U they are much broader in the non-completely-filled chain than the respective ones of the filled chain. The distance between the satellite and the band part is found to be larger than the value of U for small and intermediate values of the interaction. The results obtained support those found with second-order perturbation theory and the t-matrix approximation.
We calculate the single-particle excitation spectrum of holes in the Emery model thereby extending and improving previous calculations. The system is considered at half filling (nh{\mathit{n}}_{\mathit{h}}nh​=1, one hole per CuO2{\mathrm{CuO}}_{2}CuO2​ unit) and for hole doping, where the on-site hole-hole repulsions are kept finite. A paramagnetic form of the ground state is used. For the determination of the retarded Green's functions of copper and oxygen holes, the projection technique is applied solving the resulting equations of motions self-consistently. At half filling, the excitation spectrum exhibits a charge-transfer gap bounded by Zhang-Rice singlet states and the upper Hubbard band. Upon hole doping the flat singlet band crosses the Fermi level giving rise to a large Fermi surface at a hole concentration of nh{\mathit{n}}_{\mathit{h}}nh​=1.25. Moreover, spectral weight is shifted from the upper Hubbard band to the states near the Fermi energy. The calculated spectral densities, the singlet dispersion for the doped system, and the transfer of spectral weight are in good quantitative agreement with exact diagonalization results for 2\ifmmode\times\else\texttimes\fi{}2 CuO2{\mathrm{CuO}}_{2}CuO2​ cluster.
The two-dimensional Hubbard model is extended by placing 2S orbitals at each lattice site and studied in a systematic 1/S expansion. The 1/S results for the magnetic susceptibility and the spectra of spin-wave excitations at half-filling are consistent with the large S calculations for the Heisenberg antiferromagnet. The 1/S corrections to the fermionic spectrum lift the degeneracy along the edge of the magnetic Brillouin zone yielding minima at (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2). Relation to previous papers on the subject is discussed.
Exact results for the one-hole excitation spectra of the one-dimensional half-filled Hubbard Hamiltonian are presented. We consider short chains of N=2, 4, 6 atoms and introduce modified periodic boundary conditions which allow us to make a comparison between different N and to extrapolate the results up to infinite chains. By the increasing weight of the scattering states in the one-hole spectrum, we demonstrate a gradual disappearance of the free-electron (band) picture with increasing local electron-electron interaction U. The exact spectra of the N=6 chain verify the results of second-order perturbation theory for U/W1, where W is the bandwidth. The extrapolation to the infinite system, made with the finite-cell-scaling method, gives the gap which agrees rather well with the exact result for U/W>0.2. The average energies and weights of the band and scattering states obtained with this method for an infinite chain do not differ significantly from those of the N=6 chain.