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

Physical Review Letters

Magnetic properties of the two-dimensional Hubbard model

Liang Chen, C. Bourbonnais, T. Li, A.–M. S. Tremblay

Published Jan 1, 1991• 75 citations
Publisher

Abstract

Monte Carlo simulations of the magnetic structure factor of the two-dimensional Hubbard model are in qualitative agreement with the slave-boson approach and, in the low-temperature intermediate-coupling limit, they are in even better quantitative agreement with the random-phase approximation, as long as a renormalized repulsion U is used. This renormalization comes from maximally crossed diagrams, which account for two-body short-range correlations. One of the consequences is that Stoner ferromagnetism is not a generic property of the two-dimensional one-band Hubbard model.

DOI
10.1103/physrevlett.66.369

Related papers

Magnetism in the two-dimensional Hubbard model (abstract)

J. E. Hirsch, Hsueh‐Ju Lin

The Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.

Journal of Applied Physics•Apr 15, 1985•0 citations

Antiferromagnetism in the Two-Dimensional Hubbard Model

J. E. Hirsch, Simon Y. Tang

Magnetic properties of the two-dimensional Hubbard-model are inferred from results of Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8 and temperatures down to $T=\frac{t}{20}$ ($t=\mathrm{hopping}$) were studied. The half-filled system is found to exhibit antiferromagnetic long-range order for all values of the Coulomb repulsion $U$. The low-temperature magnetic properties are found to be well described by spin-wave theory with renormalized local moment and spin-wave velocity. Numerical evidence presented suggests that when doped the system loses the long-range order immediately away from half filling.

Physical Review Letters•Jan 30, 1989•225 citations

Two-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping

H. Q. Lin, J. E. Hirsch

We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (${t}_{2}$) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if ${t}_{2}$\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.

Physical review. B, Condensed matter•Mar 1, 1987•185 citations

Comment on ‘‘Magnetic susceptibility of the two-dimensional Hubbard model’’

Liang Chen, A.–M. S. Tremblay

The observed magnetic spin susceptibility of high-temperature superconductors such as ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ increases when x increases from zero, i.e., as one dopes away from half-filling. Recent Monte Carlo simulations of A. Moreo [Phys. Rev. B 48, 3380 (1993)] suggest that this behavior can be reproduced by the two-dimensional Hubbard model only at large coupling, namely, U/t of order 10. Using longer runs, our Monte Carlo simulations show that the same behavior as for U/t=10 is obtained even in the intermediate coupling regime (U/t=4), as long as the temperature is low enough (T=t/6) that strong antiferromagnetic correlations are building up at half-filling. These results are consistent with the fact that in two dimensions, the generalized random phase approximation should fail in the parameter range where it predicts a magnetic phase transition.

arXiv:cond-mat/9309009•Physical review. B, Condensed matter•Feb 1, 1994•4 citations

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 properties of the three-dimensional Hubbard model at half filling

A.-M. Daré, G. Albinet

We study the magnetic properties of the three-dimensional (3D) Hubbard model at half filling in the two particle self-consistent formalism, previously developed for the 2D model. We focus on the N\'eel transition approached from the disordered side and on the paramagnetic phase. We find a very good quantitative agreement with dynamical mean-field (DMF) results for the isotropic 3D model. Calculations on finite size lattices also provide satisfactory comparisons with Monte Carlo results up to the intermediate coupling regime. We point out a qualitative difference between the isotropic 3D case, and the 2D or anisotropic 3D cases for the double occupation factor. Even for this local correlation function, 2D or anisotropic 3D cases are out of reach of DMF: this comes from the inability of DMF to account for antiferromagnetic fluctuations, which are crucial.

arXiv:cond-mat/9909243•Physical review. B, Condensed matter•Feb 15, 2000•17 citations
Monte Carlo simulations of the magnetic structure factor of the two-dimensional Hubbard model are in qualitative agreement with the slave-boson approach and, in the low-temperature intermediate-coupling limit, they are in even better quantitative agreement with the random-phase approximation, as long as a renormalized repulsion U is used. This renormalization comes from maximally crossed diagrams, which account for two-body short-range correlations. One of the consequences is that Stoner ferromagnetism is not a generic property of the two-dimensional one-band Hubbard model.
The Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.
Magnetic properties of the two-dimensional Hubbard-model are inferred from results of Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8 and temperatures down to T=t20T=\frac{t}{20}T=20t​ (t=hoppingt=\mathrm{hopping}t=hopping) were studied. The half-filled system is found to exhibit antiferromagnetic long-range order for all values of the Coulomb repulsion UUU. The low-temperature magnetic properties are found to be well described by spin-wave theory with renormalized local moment and spin-wave velocity. Numerical evidence presented suggests that when doped the system loses the long-range order immediately away from half filling.
We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t2{t}_{2}t2​) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if t2{t}_{2}t2​\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.
The observed magnetic spin susceptibility of high-temperature superconductors such as ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​ increases when x increases from zero, i.e., as one dopes away from half-filling. Recent Monte Carlo simulations of A. Moreo [Phys. Rev. B 48, 3380 (1993)] suggest that this behavior can be reproduced by the two-dimensional Hubbard model only at large coupling, namely, U/t of order 10. Using longer runs, our Monte Carlo simulations show that the same behavior as for U/t=10 is obtained even in the intermediate coupling regime (U/t=4), as long as the temperature is low enough (T=t/6) that strong antiferromagnetic correlations are building up at half-filling. These results are consistent with the fact that in two dimensions, the generalized random phase approximation should fail in the parameter range where it predicts a magnetic phase transition.
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.
We study the magnetic properties of the three-dimensional (3D) Hubbard model at half filling in the two particle self-consistent formalism, previously developed for the 2D model. We focus on the N\'eel transition approached from the disordered side and on the paramagnetic phase. We find a very good quantitative agreement with dynamical mean-field (DMF) results for the isotropic 3D model. Calculations on finite size lattices also provide satisfactory comparisons with Monte Carlo results up to the intermediate coupling regime. We point out a qualitative difference between the isotropic 3D case, and the 2D or anisotropic 3D cases for the double occupation factor. Even for this local correlation function, 2D or anisotropic 3D cases are out of reach of DMF: this comes from the inability of DMF to account for antiferromagnetic fluctuations, which are crucial.