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. B, Condensed matter

Hubbard model in the strong-coupling approximation

B. M. Elrick, Mitchel D. Kovarik, Allan E. Jacobs, William G. Macready

Published Mar 1, 1993• 2 citations
Publisher

Abstract

We report numerical results for the two-dimensional Hubbard model in the strong-coupling approximation, including the three-site terms omitted in the t-J model, for a 4\ifmmode\times\else\texttimes\fi{}4 system with periodic boundary conditions. We study the one- and two-hole band structures, the root-mean-square hole-hole separation, and the hole-hole binding energy for both the t-J and the strong-coupling models. In the physical parameter region (8U/t40) believed appropriate for the high-temperature superconductors, the three-site terms enhance the hole mobility, increasing the one- and two-hole bandwidths and decreasing the binding energy, but changing the hole-hole separation only slightly; quantitative differences between the models range up to 40%. The transition (at large U/t) to the ferromagnetic Nagaoka state is sharper in the strong-coupling model; our results do not support a transition through all intermediate S values in the bulk.

DOI
10.1103/physrevb.47.6004

Related papers

Ferromagnetic domains in the large-$U$ Hubbard model with a few holes: an FCIQMC study

Yun, Sujun, Werner Dobrautz, Luo Hongjun +3 more

Two-dimensional Hubbard lattices with two or three holes are investigated as a function of $U$ in the large-$U$ limit. In the so-called Nagaoka limit (one-hole system at infinite $U$), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing $U$. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or $\frac{1}{2}$, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.

arXiv:2210.12049•Oct 21, 2022•1 citation

Single-hole properties in thet-Jand strong-coupling models

B. M. Elrick, Allan E. Jacobs

We report numerical results for the single-hole properties in the t-J model and the strong-coupling approximation to the Hubbard model in two dimensions. Using the hopping basis with over ${10}^{6}$ states we discuss (for an infinite system) the bandwidth, the leading Fourier coefficients in the dispersion, the band masses, and the spin-spin correlations near the hole. We compare our results with those obtained by other methods. The band minimum is found to be at (\ensuremath{\pi}/2,\ensuremath{\pi}/2) for the t-J model for 0.1\ensuremath{\le}t/J\ensuremath{\le}10, and for the strong-coupling model for 1\ensuremath{\le}t/J\ensuremath{\le}10. The bandwidth in both models is approximately 2J at large t/J, in rough agreement with loop-expansion results but in disagreement with other results. The strong-coupling bandwidth for t/J\ensuremath{\gtrsim}6 can be obtained from the t-J model by treating the three-site terms in first-order perturbation theory. The dispersion along the magnetic zone face is flat, giving a large parallel/perpendicular band mass ratio.

arXiv:cond-mat/9508038•Physical review. B, Condensed matter•Oct 1, 1995•6 citations

One- and two-hole excitation spectra of the Hubbard model in the non-half-filled case

Andrzej M. Oleś, Guy Tréglia, D. Spanjaard +1 more

Exact results for the one- and two-hole excitation spectra of the one- dimensional Hubbard model for filling larger than one electron per site are presented. We consider short chains of up to eight atoms and use the so-called modified periodic boundary conditions, with which we are able to extrapolate the results up to infinite chains. The one-hole excitation spectra demonstrate a gradual transition from the band picture to the spectra characterized by new satellite structures, with increasing electron-electron interaction U. The weight of the satellite part of these spectra increases with increasing U, approaching the atomic-limit value. In the ferromagnetic case, a substantial reduction of the exchange splitting is found as compared with the independent-electron approximation. The two-hole excitation spectra exhibit characteristic atomic lines at large values of U, while at intermediate values of U they are much broader in the non-completely-filled chain than the respective ones of the filled chain. The distance between the satellite and the band part is found to be larger than the value of U for small and intermediate values of the interaction. The results obtained support those found with second-order perturbation theory and the t-matrix approximation.

Physical review. B, Condensed matter•Oct 15, 1986•17 citations

Hole dynamics in a strongly correlated two-dimensional spin background

Holger Fehske, V. Waas, Heinrich Röder +1 more

In this paper we present results of finite-lattice studies of the t-J and the t-t'-J model for 18 (20) sites with up to 4 (2) holes. A modified Lanczos algorithm allowed for the classification of the ground state according to total spin S. In the one-hole sector we find evidence for the existence of hole pockets. We calculate the effective quasiparticle band and show qualitative differences between the t-J and t-t'-J model for J\ensuremath{\gtrsim}0.2. As U increases we notice a substantial band narrowing, which is maximal at the Nagaoka transition, accompanied by S-level crossings rendering a quasiparticle description difficult. In the high-doping regime we present hole binding energies for up to six holes for the t-J model. Evidence for phase separation is only found for J>t. We also studied the magnetic structure of the ground state on the 18-site lattice in the limit J=0. We present a complete ground-state classification for all numbers of holes ${\mathit{N}}_{\mathit{h}}$ and find S=${\mathit{S}}_{\mathrm{max}}$ at quarter filling in addition to the Nagaoka case.

Physical review. B, Condensed matter•Oct 15, 1991•43 citations

Ferromagnetic domains in the large- U Hubbard model with a few holes: A full configuration interaction quantum Monte Carlo study

Su-Jun Yun, Werner Dobrautz, Hongjun Luo +3 more

Two-dimensional Hubbard lattices with two or three holes are investigated as a function of $U$ in the large-$U$ limit. In the so-called Nagaoka limit (one-hole system at infinite $U$), it is known that the Hubbard model exhibits a ferromagnetic ground state. Here, by means of exact full configuration interaction quantum Monte Carlo simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing $U$. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centered on individual holes. The overall total spin of the wave functions remains the lowest possible (0 or $\frac{1}{2}$, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than 1) number of holes.

Physical review. B./Physical review. B•Feb 7, 2023•8 citations

Effect of the three-site hopping term on thet-Jmodel

Beat Ammon, Matthias Troyer, Hirokazu Tsunetsugu

We have used exact diagonalization and quantum Monte Carlo methods to study the one-dimensional t-J model including the three-site hopping term derived from the strong-coupling limit of the Hubbard model. The three-site term may be important to superconducting correlations since it allows direct hopping of local singlet electron pairs. The phase diagram is determined for several values of the strength of the three-site term and compared with that of the t-J and Hubbard models. Phase separation, which exists in the t-J model, is suppressed. In the low electron density region the formation of local singlet electron pairs is enhanced, leading to stronger superconducting correlations even for values J/t2. A large spin gap region extends from low electron densities up to high densities. In the low hole density region the superconducting correlations are suppressed at J/t>2.8 in spite of enhanced pair formation. This is because the three-site term, while enhancing the formation of electron pairs, leads to a repulsion between holes.

arXiv:cond-mat/9502037•Physical review. B, Condensed matter•Jul 1, 1995•34 citations
We report numerical results for the two-dimensional Hubbard model in the strong-coupling approximation, including the three-site terms omitted in the t-J model, for a 4\ifmmode\times\else\texttimes\fi{}4 system with periodic boundary conditions. We study the one- and two-hole band structures, the root-mean-square hole-hole separation, and the hole-hole binding energy for both the t-J and the strong-coupling models. In the physical parameter region (8U/t40) believed appropriate for the high-temperature superconductors, the three-site terms enhance the hole mobility, increasing the one- and two-hole bandwidths and decreasing the binding energy, but changing the hole-hole separation only slightly; quantitative differences between the models range up to 40%. The transition (at large U/t) to the ferromagnetic Nagaoka state is sharper in the strong-coupling model; our results do not support a transition through all intermediate S values in the bulk.
Ferromagnetic domains in the large-UUU Hubbard model with a few holes: an FCIQMC study
Two-dimensional Hubbard lattices with two or three holes are investigated as a function of UUU in the large-UUU limit. In the so-called Nagaoka limit (one-hole system at infinite UUU), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing UUU. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or 12\frac{1}{2}21​, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.
We report numerical results for the single-hole properties in the t-J model and the strong-coupling approximation to the Hubbard model in two dimensions. Using the hopping basis with over 106{10}^{6}106 states we discuss (for an infinite system) the bandwidth, the leading Fourier coefficients in the dispersion, the band masses, and the spin-spin correlations near the hole. We compare our results with those obtained by other methods. The band minimum is found to be at (\ensuremath{\pi}/2,\ensuremath{\pi}/2) for the t-J model for 0.1\ensuremath{\le}t/J\ensuremath{\le}10, and for the strong-coupling model for 1\ensuremath{\le}t/J\ensuremath{\le}10. The bandwidth in both models is approximately 2J at large t/J, in rough agreement with loop-expansion results but in disagreement with other results. The strong-coupling bandwidth for t/J\ensuremath{\gtrsim}6 can be obtained from the t-J model by treating the three-site terms in first-order perturbation theory. The dispersion along the magnetic zone face is flat, giving a large parallel/perpendicular band mass ratio.
Exact results for the one- and two-hole excitation spectra of the one- dimensional Hubbard model for filling larger than one electron per site are presented. We consider short chains of up to eight atoms and use the so-called modified periodic boundary conditions, with which we are able to extrapolate the results up to infinite chains. The one-hole excitation spectra demonstrate a gradual transition from the band picture to the spectra characterized by new satellite structures, with increasing electron-electron interaction U. The weight of the satellite part of these spectra increases with increasing U, approaching the atomic-limit value. In the ferromagnetic case, a substantial reduction of the exchange splitting is found as compared with the independent-electron approximation. The two-hole excitation spectra exhibit characteristic atomic lines at large values of U, while at intermediate values of U they are much broader in the non-completely-filled chain than the respective ones of the filled chain. The distance between the satellite and the band part is found to be larger than the value of U for small and intermediate values of the interaction. The results obtained support those found with second-order perturbation theory and the t-matrix approximation.
In this paper we present results of finite-lattice studies of the t-J and the t-t'-J model for 18 (20) sites with up to 4 (2) holes. A modified Lanczos algorithm allowed for the classification of the ground state according to total spin S. In the one-hole sector we find evidence for the existence of hole pockets. We calculate the effective quasiparticle band and show qualitative differences between the t-J and t-t'-J model for J\ensuremath{\gtrsim}0.2. As U increases we notice a substantial band narrowing, which is maximal at the Nagaoka transition, accompanied by S-level crossings rendering a quasiparticle description difficult. In the high-doping regime we present hole binding energies for up to six holes for the t-J model. Evidence for phase separation is only found for J>t. We also studied the magnetic structure of the ground state on the 18-site lattice in the limit J=0. We present a complete ground-state classification for all numbers of holes Nh{\mathit{N}}_{\mathit{h}}Nh​ and find S=Smax{\mathit{S}}_{\mathrm{max}}Smax​ at quarter filling in addition to the Nagaoka case.
Two-dimensional Hubbard lattices with two or three holes are investigated as a function of UUU in the large-UUU limit. In the so-called Nagaoka limit (one-hole system at infinite UUU), it is known that the Hubbard model exhibits a ferromagnetic ground state. Here, by means of exact full configuration interaction quantum Monte Carlo simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing UUU. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centered on individual holes. The overall total spin of the wave functions remains the lowest possible (0 or 12\frac{1}{2}21​, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than 1) number of holes.
We have used exact diagonalization and quantum Monte Carlo methods to study the one-dimensional t-J model including the three-site hopping term derived from the strong-coupling limit of the Hubbard model. The three-site term may be important to superconducting correlations since it allows direct hopping of local singlet electron pairs. The phase diagram is determined for several values of the strength of the three-site term and compared with that of the t-J and Hubbard models. Phase separation, which exists in the t-J model, is suppressed. In the low electron density region the formation of local singlet electron pairs is enhanced, leading to stronger superconducting correlations even for values J/t2. A large spin gap region extends from low electron densities up to high densities. In the low hole density region the superconducting correlations are suppressed at J/t>2.8 in spite of enhanced pair formation. This is because the three-site term, while enhancing the formation of electron pairs, leads to a repulsion between holes.