Physical Review Letters

Quasiparticle and Spin Excitation Spectra in the Normal and d -Wave Superconducting State of the Two-Dimensional Hubbard Model

Torsten Dahm, Ludwig Tewordt

Published Jan 30, 1995• 151 citations

Abstract

The quasiparticle and spin excitation spectra in the 2D Hubbard model are calculated self-consistently as functions of momentum on the real frequency axis. Near half filling we obtain in the normal state a pseudogap in the density of states. The pairing state has ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry. Below ${T}_{c}$, gaps open rapidly in the frequency spectra of the gap function, the quasiparticle scattering rate, and the density of states. The scattering rate and spin-lattice relaxation rate drop abruptly below ${T}_{c}$. Our results are consistent with experiments on ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$.

DOI: 10.1103/physrevlett.74.793

Related papers

Physical quantities in nearly antiferromagnetic and superconducting states of the two-dimensional Hubbard model and comparison with cuprate superconductors

Torsten Dahm, Ludwig Tewordt

Physical review. B, Condensed matterJul 1, 1995126 citations

Quasiparticle properties of the superconducting state of the two-dimensional Hubbard model

Emanuel Gull, Andrew J. Millis

arXiv:1412.5031Physical Review BFeb 20, 201545 citations

Incipient Antiferromagnetism and Low-Energy Excitations in the Half-Filled Two-Dimensional Hubbard Model

J. J. Deisz, D. W. Hess, Joseph W. Serene

arXiv:cond-mat/9512084Physical Review LettersFeb 19, 199684 citations

Configuration-interaction approach to the two-dimensional Hubbard model near half-filling

Barry Friedman, Gregory Levine

Physical review. B, Condensed matterApr 15, 19974 citations

Nonlocal Excitation Spectra in Two-Dimensional Doped Hubbard Model

Yoshiro Kakehashi, Peter Fulde

arXiv:0705.0581Journal of the Physical Society of JapanJun 25, 20074 citations

The Ground and Low Lying Excited States of the Two-Dimensional Hubbard Model

Yoshihiro Asai

arXiv:cond-mat/9904310Apr 22, 19990 citations

Physical Review Letters

Quasiparticle and Spin Excitation Spectra in the Normal and d -Wave Superconducting State of the Two-Dimensional Hubbard Model

Torsten Dahm, Ludwig Tewordt

Published Jan 30, 1995• 151 citations

Publisher

Abstract

{d}_{{x}^{2}\ensuremath{-}{y}^{2}}

symmetry. Below

{T}_{c}

, gaps open rapidly in the frequency spectra of the gap function, the quasiparticle scattering rate, and the density of states. The scattering rate and spin-lattice relaxation rate drop abruptly below

{T}_{c}

. Our results are consistent with experiments on

{\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}

DOI: 10.1103/physrevlett.74.793

Related papers

Physical quantities in nearly antiferromagnetic and superconducting states of the two-dimensional Hubbard model and comparison with cuprate superconductors

Torsten Dahm, Ludwig Tewordt

We have calculated within the fluctuation exchange approximation the full momentum and real-frequency dependence of the quasiparticle self-energy, the gap function, and the dynamic spin susceptibility for the two-dimensional Hubbard model near half filling. The spin-density-wave (SDW) instability is reached only asymptotically in the limit of infinite U or zero temperature. Near the SDW instability we find approximately marginal Fermi-liquid behavior, a pseudogap in the density of states, and a singlet ${\mathit{d}}_{\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ pairing instability. Below ${\mathit{T}}_{\mathit{c}}$ , gaps open rapidly in the frequency spectra of the gap function, the quasiparticle scattering rate, and the density of states. The spectral density of the dynamic spin susceptibility agrees qualitatively with the neutron-scattering data on ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4}$ . The quasiparticle scattering rate and spin-lattice relaxation rate ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ decrease rapidly below ${\mathit{T}}_{\mathit{c}}$ . The photoemission intensities along the antinode and node of the gap are in good agreement with the angle-resolved photoemission spectroscopy data on Bi 2212. Including next-nearest-neighbor hopping we obtain for sufficiently large coupling (U/t\ensuremath{\gtrsim}7) a broad commensurate neutron-scattering peak like the observed one in ${\mathrm{YBa}}_{2}$ ${\mathrm{Cu}}_{3}$ ${\mathrm{O}}_{6+\mathit{x}}$ .We have calculated within the fluctuation exchange approximation the full momentum and real-frequency dependence of the quasiparticle self-energy, the gap function, and the dynamic spin susceptibility for the two-dimensional Hubbard model near half filling. The spin-density-wave (SDW) instability is reached only asymptotically in the limit of infinite U or zero temperature. Near the SDW instability we find approximately marginal Fermi-liquid behavior, a pseudogap in the density of states, and a singlet ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ pairing instability. Below ${\mathit{T}}_{\mathit{c}}$, gaps open rapidly in the frequency spectra of the gap function, the quasiparticle scattering rate, and the density of states. The spectral density of the dynamic spin susceptibility agrees qualitatively with the neutron-scattering data on ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$. The quasiparticle scattering rate and spin-lattice relaxation rate ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ decrease rapidly below ${\mathit{T}}_{\mathit{c}}$. The photoemission intensities along the antinode and node of the gap are in good agreement with the angle-resolved photoemission spectroscopy data on Bi 2212. Including next-nearest-neighbor hopping we obtain for sufficiently large coupling (U/t\ensuremath{\gtrsim}7) a broad commensurate neutron-scattering peak like the observed one in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6+\mathit{x}}$.

Physical review. B, Condensed matterJul 1, 1995126 citations

Quasiparticle properties of the superconducting state of the two-dimensional Hubbard model

Emanuel Gull, Andrew J. Millis

Cluster dynamical mean field methods are used to calculate the normal and anomalous components of the electron self-energy of the two-dimensional Hubbard model. Issues associated with the analytical continuation of the normal and anomalous parts of the gap function are discussed. Methods of minimizing the uncertainties associated with the pseudogap-related pole in the self-energy are discussed. From these the evolution of the superconducting gap and the momentum-dependent electron spectral function across the phase diagram are determined. In the pseudogap regime, decreasing the temperature into the superconducting state leads to a decrease in the energy gap and the formation of a ``peak-dip-hump'' structure in the electronic density of states. The peak feature disperses very weakly. The calculated spectral functions are in good qualitative agreement with published data. The mathematical origin of the behavior is found to be the effect of the superconductivity on the pole structure giving rise to the normal state pseudogap. In particular the ``hump'' feature is found to arise from a zero crossing of the real part of the electron self-energy rather than from an onset of scattering. The effect of superconductivity on the zone diagonal spectra is presented.Cluster dynamical mean field methods are used to calculate the normal and anomalous components of the electron self-energy of the two-dimensional Hubbard model. Issues associated with the analytical continuation of the normal and anomalous parts of the gap function are discussed. Methods of minimizing the uncertainties associated with the pseudogap-related pole in the self-energy are discussed. From these the evolution of the superconducting gap and the momentum-dependent electron spectral function across the phase diagram are determined. In the pseudogap regime, decreasing the temperature into the superconducting state leads to a decrease in the energy gap and the formation of a ``peak-dip-hump'' structure in the electronic density of states. The peak feature disperses very weakly. The calculated spectral functions are in good qualitative agreement with published data. The mathematical origin of the behavior is found to be the effect of the superconductivity on the pole structure giving rise to the normal state pseudogap. In particular the ``hump'' feature is found to arise from a zero crossing of the real part of the electron self-energy rather than from an onset of scattering. The effect of superconductivity on the zone diagonal spectra is presented.

arXiv:1412.5031Physical Review BFeb 20, 201545 citations

Incipient Antiferromagnetism and Low-Energy Excitations in the Half-Filled Two-Dimensional Hubbard Model

J. J. Deisz, D. W. Hess, Joseph W. Serene

We present single-particle and thermodynamic properties of the half-filled single-band Hubbard model in 2D calculated in the self-consistent fluctuation exchange approximation. The low-energy excitations at moderate temperatures and small $U$ are quasiparticles with a short lifetime. As the temperature is lowered, coupling to evolving spin fluctuations leads to the extinction of these quasiparticles, signaled by a weak pseudogap in the density of states and by a positive slope in $\mathrm{Re}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})$ and a local maximum in $|\mathrm{Im}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})|$ at $\ensuremath{\varepsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. We explain these results using a simple spin-fluctuation model.We present single-particle and thermodynamic properties of the half-filled single-band Hubbard model in 2D calculated in the self-consistent fluctuation exchange approximation. The low-energy excitations at moderate temperatures and small $U$ are quasiparticles with a short lifetime. As the temperature is lowered, coupling to evolving spin fluctuations leads to the extinction of these quasiparticles, signaled by a weak pseudogap in the density of states and by a positive slope in $\mathrm{Re}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})$ and a local maximum in $|\mathrm{Im}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})|$ at $\ensuremath{\varepsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. We explain these results using a simple spin-fluctuation model.

arXiv:cond-mat/9512084Physical Review LettersFeb 19, 199684 citations

Configuration-interaction approach to the two-dimensional Hubbard model near half-filling

Barry Friedman, Gregory Levine

The two-dimensional Hubbard model near half-filling is studied using a configuration-interaction method. Superconducting order-parameter and spin-spin correlation functions are calculated as functions of distance to probe for superconductivity and antiferromagnetism. Consistent with our previous results, these more extensive calculations point toward d-wave superconductivity in the ground state of the two-dimensional repulsive Hubbard model. The d-wave correlations tend to increase with interaction strength, size of the state space used in the calculation, and doping away from half-filling. The superconducting correlations on the Fermi surface are interpreted as d-wave pairing between spin density-wave quasiparticles.The two-dimensional Hubbard model near half-filling is studied using a configuration-interaction method. Superconducting order-parameter and spin-spin correlation functions are calculated as functions of distance to probe for superconductivity and antiferromagnetism. Consistent with our previous results, these more extensive calculations point toward d-wave superconductivity in the ground state of the two-dimensional repulsive Hubbard model. The d-wave correlations tend to increase with interaction strength, size of the state space used in the calculation, and doping away from half-filling. The superconducting correlations on the Fermi surface are interpreted as d-wave pairing between spin density-wave quasiparticles.

Physical review. B, Condensed matterApr 15, 19974 citations

Nonlocal Excitation Spectra in Two-Dimensional Doped Hubbard Model

Yoshiro Kakehashi, Peter Fulde

Single-particle excitation spectra of the two-dimensional Hubbard model on the square lattice near half filling and at zero temperature are investigated on the basis of the self-consistent projection operator method. The method guarantees a high accuracy of the spectra with high energy and high momentum resolutions. It takes into account long-range intersite correlations as well as the strong on-site correlations. Effects of nonlocal excitations are clarified by comparing the results with those of the single-site approximation. The calculated spectra verify the quantum Monte-Carlo results for finite temperatures. The spectra at the Fermi level yield a hole-like Fermi surface in the underdoped region and an electron-like Fermi surface in the overdoped region. From a numerical analysis of the momentum dependent effective mass and self-energy, it is concluded that a marginal Fermi-liquid like state persists even at finite doping concentrations in the strongly correlated region because a van Hove singularity is pinned to the Fermi surface. It is also found that a kink structure appears in the quasiparticle energy band in the same region. The kink is shown to be caused by a mixing between the quasiparticle band and an excitation band with strong short-range antiferromagnetic correlations. These results suggest an explanation for some of the unusual properties of the normal state in high- $T_{\rm c}$ cuprates.Single-particle excitation spectra of the two-dimensional Hubbard model on the square lattice near half filling and at zero temperature are investigated on the basis of the self-consistent projection operator method. The method guarantees a high accuracy of the spectra with high energy and high momentum resolutions. It takes into account long-range intersite correlations as well as the strong on-site correlations. Effects of nonlocal excitations are clarified by comparing the results with those of the single-site approximation. The calculated spectra verify the quantum Monte-Carlo results for finite temperatures. The spectra at the Fermi level yield a hole-like Fermi surface in the underdoped region and an electron-like Fermi surface in the overdoped region. From a numerical analysis of the momentum dependent effective mass and self-energy, it is concluded that a marginal Fermi-liquid like state persists even at finite doping concentrations in the strongly correlated region because a van Hove singularity is pinned to the Fermi surface. It is also found that a kink structure appears in the quasiparticle energy band in the same region. The kink is shown to be caused by a mixing between the quasiparticle band and an excitation band with strong short-range antiferromagnetic correlations. These results suggest an explanation for some of the unusual properties of the normal state in high-$T_{\rm c}$ cuprates.

arXiv:0705.0581Journal of the Physical Society of JapanJun 25, 20074 citations

The Ground and Low Lying Excited States of the Two-Dimensional Hubbard Model

Yoshihiro Asai

We have studied the ground state of the two-dimensional (2D) Hubbard model by using a quantum monte method paying special attention to the shell structure effect on finite size clusters. Our calculations show there is a gap for spin excitations in the ground state and incommensurate peaks at $(π\pm δ, π)$ and $(π, π\pm δ)$ in the spin correlation function for a low lying excited state. In the ground state, the long range part of the d-wave superconducting correlation function is enhanced and the momentum distribution function at the Fermi level $(π,0)$ is rounded. The gap in spin excitations and the momentum distribution function rounding is consistent with opening a d-wave superconducting gap in the ground state.We have studied the ground state of the two-dimensional (2D) Hubbard model by using a quantum monte method paying special attention to the shell structure effect on finite size clusters. Our calculations show there is a gap for spin excitations in the ground state and incommensurate peaks at $(π\pm δ, π)$ and $(π, π\pm δ)$ in the spin correlation function for a low lying excited state. In the ground state, the long range part of the d-wave superconducting correlation function is enhanced and the momentum distribution function at the Fermi level $(π,0)$ is rounded. The gap in spin excitations and the momentum distribution function rounding is consistent with opening a d-wave superconducting gap in the ground state.

arXiv:cond-mat/9904310Apr 22, 19990 citations

{d}_{{x}^{2}\ensuremath{-}{y}^{2}}

symmetry. Below

{T}_{c}

{T}_{c}

. Our results are consistent with experiments on

{\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

pairing instability. Below

{\mathit{T}}_{\mathit{c}}

, gaps open rapidly in the frequency spectra of the gap function, the quasiparticle scattering rate, and the density of states. The spectral density of the dynamic spin susceptibility agrees qualitatively with the neutron-scattering data on ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$

{\mathrm{Sr}}_{\mathit{x}}

{\mathrm{CuO}}_{4}

. The quasiparticle scattering rate and spin-lattice relaxation rate ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ decrease rapidly below

{\mathit{T}}_{\mathit{c}}

. The photoemission intensities along the antinode and node of the gap are in good agreement with the angle-resolved photoemission spectroscopy data on Bi 2212. Including next-nearest-neighbor hopping we obtain for sufficiently large coupling (U/t\ensuremath{\gtrsim}7) a broad commensurate neutron-scattering peak like the observed one in

{\mathrm{YBa}}_{2}

{\mathrm{Cu}}_{3}

{\mathrm{O}}_{6+\mathit{x}}

U

are quasiparticles with a short lifetime. As the temperature is lowered, coupling to evolving spin fluctuations leads to the extinction of these quasiparticles, signaled by a weak pseudogap in the density of states and by a positive slope in $\mathrm{Re}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})$ and a local maximum in $|\mathrm{Im}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})|$ at $\ensuremath{\varepsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. We explain these results using a simple spin-fluctuation model.

T_{\rm c}

cuprates.

(π\pm δ, π)

and

(π, π\pm δ)

in the spin correlation function for a low lying excited state. In the ground state, the long range part of the d-wave superconducting correlation function is enhanced and the momentum distribution function at the Fermi level

(π,0)

is rounded. The gap in spin excitations and the momentum distribution function rounding is consistent with opening a d-wave superconducting gap in the ground state.