The truncated Lanczos method using a variational scheme based on Hilbert space reduction as well as a local basis change [Dagotto et al., Phys. Rev. B $58,$ 12 063 (1998)] is reexamined. The energy is extrapolated as a power-law function of the Hamiltonian variance. This systematic extrapolation procedure is tested quantitatively on the two-leg t- $J$ ladder doped with two holes. For this purpose, we have carried out calculations of the spin gap and of the pair dispersion up to size $2\ifmmode\times\else\texttimes\fi{}15.$The truncated Lanczos method using a variational scheme based on Hilbert space reduction as well as a local basis change [Dagotto et al., Phys. Rev. B $58,$ 12 063 (1998)] is reexamined. The energy is extrapolated as a power-law function of the Hamiltonian variance. This systematic extrapolation procedure is tested quantitatively on the two-leg t-$J$ ladder doped with two holes. For this purpose, we have carried out calculations of the spin gap and of the pair dispersion up to size $2\ifmmode\times\else\texttimes\fi{}15.$

arXiv:cond-mat/0010072Physical review. B, Condensed matterMar 2, 20014 citations

29a-J-7 Quasiparticle Momentum Distributions in the t-J Model

理西本, 幸則太田, R. Eder

日本物理学会講演概要集Mar 17, 19970 citations

Spectral properties of the two-dimensional Hubbard model

V. Zlatić, K. D. Schotte, Gudrun Schliecker

The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function ${\mathit{A}}_{\mathbf{p}}$ (\ensuremath{\omega}) is momentum dependent. Using ${\mathit{A}}_{\mathbf{p}}$ (\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function ${\mathit{A}}_{\mathbf{p}}$(\ensuremath{\omega}) is momentum dependent. Using ${\mathit{A}}_{\mathbf{p}}$(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.

Physical review. B, Condensed matterAug 1, 199525 citations

Single Particle Excitations in the t-J Model

Michael Brunner, C. Lavalle, Fakher F. Assaad +1 more

Springer eBooksJan 1, 20010 citations

Polarons and bipolarons in strongly interacting electron-phonon systems

Gerhard Wellein, Heinrich Röder, Holger Fehske

The Holstein Hubbard and Holstein t-J models are studied for a wide range of phonon frequencies, electron-electron, and electron-phonon interaction strengths on finite lattices with up to ten sites by means of direct Lanczos diagonalization. Previously the necessary truncation of the phononic Hilbert space caused serious limitations to either very small systems (four or even two sites) or to weak electron-phonon coupling, in particular in the adiabatic regime. Using parallel computers we were able to investigate the transition from ``large'' to ``small'' polarons in detail. By resolving the low-lying eigenstates of the Hamiltonian and by calculating the spectral function, we can identify a polaron band in the strong-coupling case, whose dispersion deviates from the free-particle dispersion at low and intermediate phonon frequencies. For two electrons (holes) we establish the existence of bipolaronic states and discuss the formation of a bipolaron band. For the two-dimensional Holstein t-J model, we demonstrate that the formation of hole polarons is favored by strong Coulomb correlations. Analyzing hole-hole correlation functions, we find that hole binding is enhanced as a dynamical effect of the electron-phonon interaction. \textcopyright{} 1996 The American Physical Society.The Holstein Hubbard and Holstein t-J models are studied for a wide range of phonon frequencies, electron-electron, and electron-phonon interaction strengths on finite lattices with up to ten sites by means of direct Lanczos diagonalization. Previously the necessary truncation of the phononic Hilbert space caused serious limitations to either very small systems (four or even two sites) or to weak electron-phonon coupling, in particular in the adiabatic regime. Using parallel computers we were able to investigate the transition from ``large'' to ``small'' polarons in detail. By resolving the low-lying eigenstates of the Hamiltonian and by calculating the spectral function, we can identify a polaron band in the strong-coupling case, whose dispersion deviates from the free-particle dispersion at low and intermediate phonon frequencies. For two electrons (holes) we establish the existence of bipolaronic states and discuss the formation of a bipolaron band. For the two-dimensional Holstein t-J model, we demonstrate that the formation of hole polarons is favored by strong Coulomb correlations. Analyzing hole-hole correlation functions, we find that hole binding is enhanced as a dynamical effect of the electron-phonon interaction. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9512143Physical review. B, Condensed matterApr 15, 1996163 citations

The truncated Lanczos method using a variational scheme based on Hilbert space reduction as well as a local basis change [Dagotto et al., Phys. Rev. B

58,

12 063 (1998)] is reexamined. The energy is extrapolated as a power-law function of the Hamiltonian variance. This systematic extrapolation procedure is tested quantitatively on the two-leg t-

J

ladder doped with two holes. For this purpose, we have carried out calculations of the spin gap and of the pair dispersion up to size $2\ifmmode\times\else\texttimes\fi{}15.$

{\mathit{A}}_{\mathbf{p}}

(\ensuremath{\omega}) is momentum dependent. Using

{\mathit{A}}_{\mathbf{p}}

(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.