arXiv:cond-mat/9501119 · Physical Review Letters

Spectral Weight Function for the Half-Filled Hubbard Model: A Singular Value Decomposition Approach

C. E. Creffield, Elyakum G. Klepfish, Edward R. Pike, Sarben Sarkar

Published Jul 17, 1995• 57 citations

Abstract

The singular value decomposition technique is used to reconstruct the electronic spectral weight function for a half-filled Hubbard model with on-site repulsion $U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4t$ from quantum Monte Carlo data. A two-band structure for the single-particle excitation spectrum is found to persist as the lattice size exceeds the spin-spin correlation length. The observed bands are flat in the vicinity of the $(0,\ensuremath{\pi}),(\ensuremath{\pi},0)$ points in the Brillouin zone, in accordance with experimental data for high-temperature superconducting compounds.

DOI: 10.1103/physrevlett.75.517

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Spectral Weight Function and Charge-Excitation Gap of the Half-Filled 2D Hubbard Model

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arXiv:cond-mat/9501119 · Physical Review Letters

Spectral Weight Function for the Half-Filled Hubbard Model: A Singular Value Decomposition Approach

C. E. Creffield, Elyakum G. Klepfish, Edward R. Pike, Sarben Sarkar

Published Jul 17, 1995• 57 citations

arXiv HTML PDF

Abstract

The singular value decomposition technique is used to reconstruct the electronic spectral weight function for a half-filled Hubbard model with on-site repulsion

U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4t

from quantum Monte Carlo data. A two-band structure for the single-particle excitation spectrum is found to persist as the lattice size exceeds the spin-spin correlation length. The observed bands are flat in the vicinity of the

(0,\ensuremath{\pi}),(\ensuremath{\pi},0)

points in the Brillouin zone, in accordance with experimental data for high-temperature superconducting compounds.

DOI: 10.1103/physrevlett.75.517

Related papers

Two-site correlation in analysis of the Hubbard model

Hideki Matsumoto, Ferdinando Mancini

Electronic states of a two-dimensional Hubbard model near half filling is investigated by use of the composite-operator method, which is improved by including two-site correlations in combined use with the resolvent method. The densities of states obtained for the upper and lower Hubbard bands have three-peek structures at half filling and give shapes above a certain temperature similar to the ones obtained in the numerical simulation by Dagotto, Ortolani, and Scalapino [Phys. Rev. B 46, 3183 (1992)], but show narrowing of the bands at low temperature due to the formation of spin-singlet states among the nearest-neighbor electrons. A doped case shows a coherent peak at the Fermi level and the feature of the density of states is very similar to the one from numerical simulation. The one-particle spectra in the (k,k) direction is also presented. The results show that, at half filling, the spectral weight is not evenly distributed between two bands; most of the weight of the lower Hubbard band appears between (0,0) and (\ensuremath{\pi}/2a,\ensuremath{\pi}/2a), while that of the upper Hubbard band lies in the region between (\ensuremath{\pi}/2a,\ensuremath{\pi}/2a) and (\ensuremath{\pi}/a,\ensuremath{\pi}/a), keeping roughly the original band distribution. With hole doping, a flat band develops at the Fermi level with a large Fermi surface and the lower Hubbard band extends through the whole Brillouin zone.Electronic states of a two-dimensional Hubbard model near half filling is investigated by use of the composite-operator method, which is improved by including two-site correlations in combined use with the resolvent method. The densities of states obtained for the upper and lower Hubbard bands have three-peek structures at half filling and give shapes above a certain temperature similar to the ones obtained in the numerical simulation by Dagotto, Ortolani, and Scalapino [Phys. Rev. B 46, 3183 (1992)], but show narrowing of the bands at low temperature due to the formation of spin-singlet states among the nearest-neighbor electrons. A doped case shows a coherent peak at the Fermi level and the feature of the density of states is very similar to the one from numerical simulation. The one-particle spectra in the (k,k) direction is also presented. The results show that, at half filling, the spectral weight is not evenly distributed between two bands; most of the weight of the lower Hubbard band appears between (0,0) and (\ensuremath{\pi}/2a,\ensuremath{\pi}/2a), while that of the upper Hubbard band lies in the region between (\ensuremath{\pi}/2a,\ensuremath{\pi}/2a) and (\ensuremath{\pi}/a,\ensuremath{\pi}/a), keeping roughly the original band distribution. With hole doping, a flat band develops at the Fermi level with a large Fermi surface and the lower Hubbard band extends through the whole Brillouin zone.

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Spectral function of holes in the Emery model

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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.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.

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Spectral weight function for the two-dimensional Hubbard model

Steven R. White

We present results for the single-particle spectral weight function for the two-dimensional Hubbard model. Results were obtained using analytic expressions for the first two moments of the spectral weight function, along with numerical calculations using a combination of quantum Monte Carlo and the maximum-entropy method of analytic continuation. The expressions for the first two moments are surprisingly simple, involving only the parameters of the model, the chemical potential, and the filling. At half-filling, the squared width (variance) of the spectral weight is exactly ${\mathit{U}}^{2}$ /4. Numerical results are shown for 8\ifmmode\times\else\texttimes\fi{}8 lattices at a variety of fillings and momenta. The insulating antiferromagnetic gap in the spectral weights, readily apparent in the results at half-filling, is absent at a filling of 0.95.We present results for the single-particle spectral weight function for the two-dimensional Hubbard model. Results were obtained using analytic expressions for the first two moments of the spectral weight function, along with numerical calculations using a combination of quantum Monte Carlo and the maximum-entropy method of analytic continuation. The expressions for the first two moments are surprisingly simple, involving only the parameters of the model, the chemical potential, and the filling. At half-filling, the squared width (variance) of the spectral weight is exactly ${\mathit{U}}^{2}$/4. Numerical results are shown for 8\ifmmode\times\else\texttimes\fi{}8 lattices at a variety of fillings and momenta. The insulating antiferromagnetic gap in the spectral weights, readily apparent in the results at half-filling, is absent at a filling of 0.95.

Physical review. B, Condensed matterSep 1, 199185 citations

The singular value decomposition technique is used to reconstruct the electronic spectral weight function for a half-filled Hubbard model with on-site repulsion

U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4t

(0,\ensuremath{\pi}),(\ensuremath{\pi},0)

points in the Brillouin zone, in accordance with experimental data for high-temperature superconducting compounds.

We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion

U

at half-filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of

U

is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$ and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit $U\ensuremath{\rightarrow}0$. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and $\ensuremath{\eta}$-spin

\text{SU}(2)

rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at

U=0

. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a van Hove singularity that persists as a consequence of integrability.

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.

{\mathit{U}}^{2}

/4. Numerical results are shown for 8\ifmmode\times\else\texttimes\fi{}8 lattices at a variety of fillings and momenta. The insulating antiferromagnetic gap in the spectral weights, readily apparent in the results at half-filling, is absent at a filling of 0.95.