Influence of next-nearest-neighbor electron hopping on the magnetic properties of the 2D Hubbard model

Daniel Duffy, Adrianna Moreo

Published Dec 31, 1996• 0 citations

Abstract

Comparing experimental data for high temperature cuprate superconductors with numerical results for electronic models, it is becoming apparent that a diagonal hopping has to be included to obtain quantitative agreement. According to recent estimations the value of the diagonal hopping, t{prime}, appears to be material dependent. However, the values for t{prime} discussed in the literature were obtained comparing theoretical results in the non-interacting and weak-coupling limit with experimental photoemission data. The goal of this paper is to study how t{prime} gets renormalized as the interaction between electrons, U, increases. For this purpose, the effect of adding a bare diagonal hopping t{prime} to the fully interacting two dimensional Hubbard model Hamiltonian is investigated using numerical techniques. Positive and negative values of t{prime} are analyzed. Magnetic correlations and incommensurability are studied for values of U/t ranging from 0 to 6, and as a function of the electronic density.

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Influence of next-nearest-neighbor electron hopping on the magnetic properties of the 2D Hubbard model

Daniel Duffy, Adrianna Moreo

Published Dec 31, 1996• 0 citations

OpenAlex

Abstract

Related papers

Influence of next-nearest-neighbor electron hopping on the static and dynamical properties of the two-dimensional Hubbard model

Daniel Duffy, Adriana Moreo

Comparing experimental data for high- ${\mathit{T}}_{\mathit{c}}$ cuprate superconductors with numerical results for electronic models, it is becoming apparent that a hopping along the plaquette diagonals has to be included to obtain quantitative agreement. However, the values for ${\mathit{t}}^{\ensuremath{'}}$ discussed in the literature were obtained comparing theoretical results in the weak-coupling limit with photoemission data and band-structure calculations. The goal of this paper is to study how ${\mathit{t}}^{\ensuremath{'}}$ gets renormalized as the interaction between electrons, U, increases. For this purpose, the effect of adding a bare diagonal hopping ${\mathit{t}}^{\ensuremath{'}}$ to the two-dimensional Hubbard model Hamiltonian is investigated using numerical techniques. Spin-spin correlations, n(k), 〈n〉 vs \ensuremath{\mu}, and local magnetic moments are studied for several values of U/t and the electronic density. The spectral function A(k,\ensuremath{\omega}) is also discussed. We introduce a criterion to determine probable locations of Fermi surfaces at zero temperature. In general, we conclude that it is very dangerous to extract a bare parameter of the Hamiltonian (${\mathit{t}}^{\ensuremath{'}}$) from photoemission spectroscopy data where renormalized parameters play the important role.Comparing experimental data for high-${\mathit{T}}_{\mathit{c}}$ cuprate superconductors with numerical results for electronic models, it is becoming apparent that a hopping along the plaquette diagonals has to be included to obtain quantitative agreement. However, the values for ${\mathit{t}}^{\ensuremath{'}}$ discussed in the literature were obtained comparing theoretical results in the weak-coupling limit with photoemission data and band-structure calculations. The goal of this paper is to study how ${\mathit{t}}^{\ensuremath{'}}$ gets renormalized as the interaction between electrons, U, increases. For this purpose, the effect of adding a bare diagonal hopping ${\mathit{t}}^{\ensuremath{'}}$ to the two-dimensional Hubbard model Hamiltonian is investigated using numerical techniques. Spin-spin correlations, n(k), 〈n〉 vs \ensuremath{\mu}, and local magnetic moments are studied for several values of U/t and the electronic density. The spectral function A(k,\ensuremath{\omega}) is also discussed. We introduce a criterion to determine probable locations of Fermi surfaces at zero temperature. In general, we conclude that it is very dangerous to extract a bare parameter of the Hamiltonian (${\mathit{t}}^{\ensuremath{'}}$) from photoemission spectroscopy data where renormalized parameters play the important role.

arXiv:cond-mat/9506083Physical review. B, Condensed matterDec 1, 199567 citations

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

A. Sherman, Michael Schreiber

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

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Physical review. B, Condensed matterMar 1, 1987185 citations

Magnetic and pair correlations of the Hubbard model with next-nearest-neighbor hopping

Alain Veilleux, A.-M. Daré, Liang Chen +2 more

A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$=-0.35t as a model for high-temperature superconductors. Magnetic properties are analyzed using the two-particle self-consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite ${\mathit{t}}^{\ensuremath{'}}$ and at ${\mathit{t}}^{\ensuremath{'}}$=0 but for two totally different physical reasons. When ${\mathit{t}}^{\ensuremath{'}}$=0, it is induced by antiferromagnetic correlations while at ${\mathit{t}}^{\ensuremath{'}}$=-0.35t it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with T-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the d-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed.A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$=-0.35t as a model for high-temperature superconductors. Magnetic properties are analyzed using the two-particle self-consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite ${\mathit{t}}^{\ensuremath{'}}$ and at ${\mathit{t}}^{\ensuremath{'}}$=0 but for two totally different physical reasons. When ${\mathit{t}}^{\ensuremath{'}}$=0, it is induced by antiferromagnetic correlations while at ${\mathit{t}}^{\ensuremath{'}}$=-0.35t it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with T-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the d-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed.

arXiv:cond-mat/9507045Physical review. B, Condensed matterDec 1, 199540 citations

Effects of the next-nearest-neighbor hopping on the low-dimensional Hubbard model: ferromagnetism, antiferromagnetism, and superconductivity

Luhang Yang, Adrian E. Feiguin, Thomas Devereaux +1 more

The Hubbard model has attracted considerable interest due to its prototypical role in describing strongly interacting electronic systems, such as high-critical-temperature superconductors as well as many novel quantum materials. By introducing next-nearest-neighbor (NNN) hoppings to the Hubbard model, the phase diagram becomes richer, and fascinating phenomena arise in both, one-dimensional chains and square lattices, such as: antiferromagnetism, ferromagnetism, superconductivity (SC), as well as charge orders, among others. Moreover, NNN hoppings play a fundamental role in understanding effects of doping on magnetism and pairing orders in strongly interacting regimes. In this article, we review the recent progress in understanding the different competing phases of this model in one and two dimensions from a computational perspective. We comment on the pressing technical challenges, illustrate the controversial results concerning the emergence of the SC phase, and conclude with our perspectives on future explorations.The Hubbard model has attracted considerable interest due to its prototypical role in describing strongly interacting electronic systems, such as high-critical-temperature superconductors as well as many novel quantum materials. By introducing next-nearest-neighbor (NNN) hoppings to the Hubbard model, the phase diagram becomes richer, and fascinating phenomena arise in both, one-dimensional chains and square lattices, such as: antiferromagnetism, ferromagnetism, superconductivity (SC), as well as charge orders, among others. Moreover, NNN hoppings play a fundamental role in understanding effects of doping on magnetism and pairing orders in strongly interacting regimes. In this article, we review the recent progress in understanding the different competing phases of this model in one and two dimensions from a computational perspective. We comment on the pressing technical challenges, illustrate the controversial results concerning the emergence of the SC phase, and conclude with our perspectives on future explorations.

arXiv:2511.13534Journal of Physics Condensed MatterDec 23, 20250 citations

D-Wave Pairing of the Two-Dimensional Extended t-J Model

C. T. Shih, Y. C. Chen, Taehyun Lee

In this paper, the effect of the next-earest (t ′ ) and third-earest (t ′ ′ ) hopping terms on superconductivity (SC) of the two-dimensional (2D) extended t-J model is studied by the variational Monte-Carlo (VMC) method. For hole-doped systems, the d-wave pairing correlation is suppressed by t ′ and t ′ ′ for underdoped cases, while it can be greatly enhanced by proper values of t ′ and t ′ ′ for the overdoped ones. This behavior results from the deformation of the Fermi surfaces. PACS numbers: 74.20.-z, 71.18.+y The 2D t-J model is one of the most popular models for studying the properties of the high-temperature superconductivity (HTS) [1, 2]. Yet the problem whether this model can give such high Tc for the cuprates or not is still under debate [4–7]. It has been well accepted that the next-nearest-neighbor (t ′ ) and the third-nearest-neighbor (t ′ ′) hopping terms are necessary for models to explain several experiments like angle-resolved photoemission (ARPES) of HTS [3]. However, the effect of t ′ and t ′ ′ on pairing correlation is also controversial. Previous DMRG studies of the two-dimensional (2D) extended t-J model show that the SC is suppressed (enhanced) for negative (positive) next-nearestneighbor hopping t ′ /t [8]. But results from first-principle calculation show that t ′ /t = −0.3 maximizes SC at optimal doping [9]. The Hamiltonian of the extended t-J model is H = Ht + HJ = − ∑ ij tij(˜c † i,σ ˜cj,σ + H.C.) + J ∑In this paper, the effect of the next-earest (t ′ ) and third-earest (t ′ ′ ) hopping terms on superconductivity (SC) of the two-dimensional (2D) extended t-J model is studied by the variational Monte-Carlo (VMC) method. For hole-doped systems, the d-wave pairing correlation is suppressed by t ′ and t ′ ′ for underdoped cases, while it can be greatly enhanced by proper values of t ′ and t ′ ′ for the overdoped ones. This behavior results from the deformation of the Fermi surfaces. PACS numbers: 74.20.-z, 71.18.+y The 2D t-J model is one of the most popular models for studying the properties of the high-temperature superconductivity (HTS) [1, 2]. Yet the problem whether this model can give such high Tc for the cuprates or not is still under debate [4–7]. It has been well accepted that the next-nearest-neighbor (t ′ ) and the third-nearest-neighbor (t ′ ′) hopping terms are necessary for models to explain several experiments like angle-resolved photoemission (ARPES) of HTS [3]. However, the effect of t ′ and t ′ ′ on pairing correlation is also controversial. Previous DMRG studies of the two-dimensional (2D) extended t-J model show that the SC is suppressed (enhanced) for negative (positive) next-nearestneighbor hopping t ′ /t [8]. But results from first-principle calculation show that t ′ /t = −0.3 maximizes SC at optimal doping [9]. The Hamiltonian of the extended t-J model is H = Ht + HJ = − ∑ ij tij(˜c † i,σ ˜cj,σ + H.C.) + J ∑

Chinese Journal of PhysicsJun 1, 20050 citations

Comparing experimental data for high-

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

cuprate superconductors with numerical results for electronic models, it is becoming apparent that a hopping along the plaquette diagonals has to be included to obtain quantitative agreement. However, the values for ${\mathit{t}}^{\ensuremath{'}}$ discussed in the literature were obtained comparing theoretical results in the weak-coupling limit with photoemission data and band-structure calculations. The goal of this paper is to study how ${\mathit{t}}^{\ensuremath{'}}$ gets renormalized as the interaction between electrons, U, increases. For this purpose, the effect of adding a bare diagonal hopping ${\mathit{t}}^{\ensuremath{'}}$ to the two-dimensional Hubbard model Hamiltonian is investigated using numerical techniques. Spin-spin correlations, n(k), 〈n〉 vs \ensuremath{\mu}, and local magnetic moments are studied for several values of U/t and the electronic density. The spectral function A(k,\ensuremath{\omega}) is also discussed. We introduce a criterion to determine probable locations of Fermi surfaces at zero temperature. In general, we conclude that it is very dangerous to extract a bare parameter of the Hamiltonian (${\mathit{t}}^{\ensuremath{'}}$) from photoemission spectroscopy data where renormalized parameters play the important role.

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.