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/9602135 · Journal of Physics Condensed Matter

Frequency-dependent spin susceptibility in the two-dimensional Hubbard model

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

Published May 5, 1997• 1 citation
arXivHTMLPDF

Abstract

A Quantum Monte Carlo calculation of dynamical spin susceptibility in the half-filled 2D Hubbard model is presented for temperature $T=0.2t$ and an intermediate on-site repulsion $U=4t$. Using the singular value decomposition technique we succeed in analytically continuing the Matsubara Green's function into the real frequency domain and in deriving the spectral representation for the longitudinal and transverse spin susceptibility. The simulation results, while contradicting the random-phase approximation prediction of antiferromagnetic long-range order at this temperature, are in agreement with an extension of a self-consistent renormalization approach of Moriya. The static susceptibility calculated using this technique is qualitatively consistent with the $ω\rightarrow 0 $ simulation results.

DOI
10.1088/0953-8984/9/18/003

Related papers

Magnetic susceptibility of the two-dimensional Hubbard model

Adriana Moreo

Using quantum Monte Carlo techniques we study the magnetic susceptibility of the Hubbard model on a two-dimensional square lattice for values of the coupling U/t ranging from 4 to 20, and as a function of temperature and doping. For U/t=4 the magnetic susceptibility has a maximum at half filling and decreases with doping, in qualitative agreement with recent random-phase-approximation calculations. However, for U/t=10 the susceptibility increases with hole doping near half filling resembling the experimental results obtained for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$. At low electronic density the temperature dependence of the susceptibility is compatible with that of a Fermi liquid.

Physical review. B, Condensed matter•Aug 1, 1993•39 citations

Magnetic susceptibility of the two-dimensional Hubbard model using a power series for the hopping constant

A. Sherman, Michael Schreiber

The magnetic susceptibility of the two-dimensional repulsive Hubbard model with nearest-neighbor hopping is investigated using the diagram technique developed for the case of strong correlations. In this technique, a power series in the hopping constant is used. At half-filling, the calculated zero-frequency susceptibility and the square of the site spin reproduce adequately the results of Monte Carlo simulations. Also, in agreement with numerical simulations, no evidence of ferromagnetic correlations was found in the considered range of electron concentrations $0.8\ensuremath{\lesssim}\overline{n}\ensuremath{\lesssim}1.2$ for the repulsion parameters $8\ensuremath{\mid}t\ensuremath{\mid}\ensuremath{\leqslant}U\ensuremath{\leqslant}16\ensuremath{\mid}t\ensuremath{\mid}$. However, for larger $U∕\ensuremath{\mid}t\ensuremath{\mid}$ and $\ensuremath{\mid}1\ensuremath{-}\overline{n}\ensuremath{\mid}\ensuremath{\approx}0.2$, the nearest-neighbor correlations become ferromagnetic. For $\overline{n}\ensuremath{\lesssim}0.94$ and $\overline{n}\ensuremath{\gtrsim}1.06$, the imaginary part of the real-frequency susceptibility becomes incommensurate for small frequencies. The incommensurability parameter grows with departure from half-filling and decreases with increasing frequency. This behavior of the susceptibility can explain the observed low-frequency incommensurate response observed in normal-state lanthanum cuprates.

arXiv:0707.0584•Physical Review B•Dec 14, 2007•14 citations

Monte Carlo Study of the Two-Dimensional Hubbard Model

J. E. Hirsch

A two-dimensional model of interacting electrons on a lattice, the Hubbard model, has been studied by means of a numerical simulation technique. Results for the half-filled-band sector are presented for lattices of up to 6\ifmmode\times\else\texttimes\fi{}6 spatial sites, as a function of temperature and electron-electron repulsion $U$. In the ground state, the system is found to exhibit antiferromagnetic long-range order for all values of $U$, although greatly reduced from the mean-field-theory predictions.

Physical Review Letters•Nov 14, 1983•77 citations

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

C. E. Creffield, Elyakum G. Klepfish, Edward R. Pike +1 more

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.

arXiv:cond-mat/9501119•Physical Review Letters•Jul 17, 1995•57 citations

Comparison of Monte Carlo and diagrammatic calculations for the two-dimensional Hubbard model

Niyazi Bulut, Douglas J. Scalapino, Steven R. White

Monte Carlo results for a two-dimensional Hubbard model in the intermediate-coupling regime U=4t are compared with a diagrammatic spin-fluctuation approximation. Simulations on an 8\ifmmode\times\else\texttimes\fi{}8 lattice doped away from half filling were carried out down to temperatures of order 140 of the bandwidth. Results for the spin susceptibility \ensuremath{\chi}(q,i\ensuremath{\omega}${}_{\mathrm{m}}$), the electron self-energy \ensuremath{\Sigma}(p,i\ensuremath{\omega}${}_{\mathrm{n}}$), various pair-field susceptibilities, and the irreducible particle-particle scattering vertex \ensuremath{\Gamma}(p\ensuremath{'},i\ensuremath{\omega}${}_{\mathrm{n}\ensuremath{'}}$|p,i\ensuremath{\omega}${}_{\mathrm{n}}$) were obtained. A random-phase approximation for \ensuremath{\chi}(q,i\ensuremath{\omega}${}_{\mathrm{m}}$) with a renormalized Coulomb coupling U\ifmmode\bar\else\textasciimacron\fi{} is shown to provide a fit to the Monte Carlo data. A similar approximation for the Berk-Schrieffer spin-fluctuation interaction also provides a reasonable fit to the self-energy \ensuremath{\Sigma}(p,i\ensuremath{\omega}${}_{\mathrm{n}}$) in the region explored by the Monte Carlo data. However, a similar approximation for the irreducible particle-particle interaction failed to reproduce the Monte Carlo results. Higher-order vertex corrections were calculated, but significant discrepancies with Monte Carlo results for \ensuremath{\Gamma} remain.

Physical review. B, Condensed matter•Feb 1, 1993•103 citations

Spin Waves in the Half-Filled Hubbard Model beyond the Random Phase Approximation

P. J. H. Denteneer, J. M. J. van Leeuwen

The velocity of long-wavelength spin waves for the two-dimensional Hubbard model on a square lattice at half-filling is calculated using the variational Monte Carlo method with a Gutzwiller-type wave function. We show that the result from the Random Phase Approximation (RPA) for the spin wave velocity can also be found as the square root of the ratio of the helicity modulus and the perpendicular susceptibility as calculated in the Hartree-Fock approximation (HFA). Since the Gutzwiller wave function improves upon the HFA, our result for the spin wave velocity improves upon the RPA result. For the on-site repulsion U between 3 and 12 times the hopping integral t the spin wave velocity increases by 34 to 15% compared to the RPA result.

Europhysics Letters (EPL)•May 20, 1993•9 citations
A Quantum Monte Carlo calculation of dynamical spin susceptibility in the half-filled 2D Hubbard model is presented for temperature T=0.2tT=0.2tT=0.2t and an intermediate on-site repulsion U=4tU=4tU=4t. Using the singular value decomposition technique we succeed in analytically continuing the Matsubara Green's function into the real frequency domain and in deriving the spectral representation for the longitudinal and transverse spin susceptibility. The simulation results, while contradicting the random-phase approximation prediction of antiferromagnetic long-range order at this temperature, are in agreement with an extension of a self-consistent renormalization approach of Moriya. The static susceptibility calculated using this technique is qualitatively consistent with the ω→0ω\rightarrow 0 ω→0 simulation results.
Using quantum Monte Carlo techniques we study the magnetic susceptibility of the Hubbard model on a two-dimensional square lattice for values of the coupling U/t ranging from 4 to 20, and as a function of temperature and doping. For U/t=4 the magnetic susceptibility has a maximum at half filling and decreases with doping, in qualitative agreement with recent random-phase-approximation calculations. However, for U/t=10 the susceptibility increases with hole doping near half filling resembling the experimental results obtained for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​. At low electronic density the temperature dependence of the susceptibility is compatible with that of a Fermi liquid.
The magnetic susceptibility of the two-dimensional repulsive Hubbard model with nearest-neighbor hopping is investigated using the diagram technique developed for the case of strong correlations. In this technique, a power series in the hopping constant is used. At half-filling, the calculated zero-frequency susceptibility and the square of the site spin reproduce adequately the results of Monte Carlo simulations. Also, in agreement with numerical simulations, no evidence of ferromagnetic correlations was found in the considered range of electron concentrations $0.8\ensuremath{\lesssim}\overline{n}\ensuremath{\lesssim}1.2$ for the repulsion parameters $8\ensuremath{\mid}t\ensuremath{\mid}\ensuremath{\leqslant}U\ensuremath{\leqslant}16\ensuremath{\mid}t\ensuremath{\mid}$. However, for larger $U∕\ensuremath{\mid}t\ensuremath{\mid}$ and $\ensuremath{\mid}1\ensuremath{-}\overline{n}\ensuremath{\mid}\ensuremath{\approx}0.2$, the nearest-neighbor correlations become ferromagnetic. For $\overline{n}\ensuremath{\lesssim}0.94$ and $\overline{n}\ensuremath{\gtrsim}1.06$, the imaginary part of the real-frequency susceptibility becomes incommensurate for small frequencies. The incommensurability parameter grows with departure from half-filling and decreases with increasing frequency. This behavior of the susceptibility can explain the observed low-frequency incommensurate response observed in normal-state lanthanum cuprates.
A two-dimensional model of interacting electrons on a lattice, the Hubbard model, has been studied by means of a numerical simulation technique. Results for the half-filled-band sector are presented for lattices of up to 6\ifmmode\times\else\texttimes\fi{}6 spatial sites, as a function of temperature and electron-electron repulsion UUU. In the ground state, the system is found to exhibit antiferromagnetic long-range order for all values of UUU, although greatly reduced from the mean-field-theory predictions.
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=4tU\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4tU=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.
Monte Carlo results for a two-dimensional Hubbard model in the intermediate-coupling regime U=4t are compared with a diagrammatic spin-fluctuation approximation. Simulations on an 8\ifmmode\times\else\texttimes\fi{}8 lattice doped away from half filling were carried out down to temperatures of order 140 of the bandwidth. Results for the spin susceptibility \ensuremath{\chi}(q,i\ensuremath{\omega}m{}_{\mathrm{m}}m​), the electron self-energy \ensuremath{\Sigma}(p,i\ensuremath{\omega}n{}_{\mathrm{n}}n​), various pair-field susceptibilities, and the irreducible particle-particle scattering vertex \ensuremath{\Gamma}(p\ensuremath{'},i\ensuremath{\omega}${}_{\mathrm{n}\ensuremath{'}}$|p,i\ensuremath{\omega}n{}_{\mathrm{n}}n​) were obtained. A random-phase approximation for \ensuremath{\chi}(q,i\ensuremath{\omega}m{}_{\mathrm{m}}m​) with a renormalized Coulomb coupling U\ifmmode\bar\else\textasciimacron\fi{} is shown to provide a fit to the Monte Carlo data. A similar approximation for the Berk-Schrieffer spin-fluctuation interaction also provides a reasonable fit to the self-energy \ensuremath{\Sigma}(p,i\ensuremath{\omega}n{}_{\mathrm{n}}n​) in the region explored by the Monte Carlo data. However, a similar approximation for the irreducible particle-particle interaction failed to reproduce the Monte Carlo results. Higher-order vertex corrections were calculated, but significant discrepancies with Monte Carlo results for \ensuremath{\Gamma} remain.
The velocity of long-wavelength spin waves for the two-dimensional Hubbard model on a square lattice at half-filling is calculated using the variational Monte Carlo method with a Gutzwiller-type wave function. We show that the result from the Random Phase Approximation (RPA) for the spin wave velocity can also be found as the square root of the ratio of the helicity modulus and the perpendicular susceptibility as calculated in the Hartree-Fock approximation (HFA). Since the Gutzwiller wave function improves upon the HFA, our result for the spin wave velocity improves upon the RPA result. For the on-site repulsion U between 3 and 12 times the hopping integral t the spin wave velocity increases by 34 to 15% compared to the RPA result.