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

Bulletin of Pure & Applied Sciences- Physics

High-Tc Superconductivity within t - t'- J - J' Model

K. Roy, Nanda Kumar Ghosh

Published Jan 1, 2021• 3 citations
Publisher

Abstract

The behaviour of high-Tc cuprates in its ground state has been examined within the t-t'-J-J' model using an exact method. The role of next-nearest-neighbor (NNN) hopping (t') and exchange (J') interactions on the charge gap, spin gap and effective exchange interaction has been investigated. Charge gap shows a gapped behavior. Spin gap curves establish a gapless behavior at small t'/t and J'/t. Also, it appears that effective exchange interaction is very much relevant in the present system

DOI
10.5958/2320-3218.2021.00004.x

Related papers

Signatures of next-nearest-neighbor (NNN) Antiferromagnetic Exchange Interaction on High-Tc Superconductivity Within t-t'-J-J' Model

K Roy, Papiya Pal, Nanda Kumar Ghosh

The influence of the next-nearest-neighbor (NNN) antiferromagnetic interaction J ’has been examined within t-t'-J-J ’model in an exact technique. An 8-site square cluster is chosen as the representative of the system. The effect of the next-nearest-neighbor (NNN) antiferromagnetic interaction on various ground state properties such as electron-electron correlation, spin-spin correlation, effective hopping amplitude etc. has been studied. Temperature variation of the susceptibility shows that J ’suppresses short range antiferromagnetic order. Applying periodic boundary conditions, the calculations have been extended beyond the 8-site limit.

Bulletin of Pure & Applied Sciences- Physics•Jan 1, 2018•2 citations

High-Tc superconductivity within t-J-V-Vʹ model

Srijani Ghosh, Krishanu Roy, Nanda Kumar Ghosh

We present numerical results on the role of next-nearest-neighbor (NNN) Coulomb repulsion within t-J-V-Vʹ model using exact diagonalization (ED) technique within an 8 – site tilted square cluster at a hole doping <h>=0.25. Periodic boundary conditions have been applied to obtain complete basis states. It appears that hole-hole correlation is dominant at d = √2. NNN Coulomb repulsion localizes the electrons and cooperates with exchange interaction J. Non-Fermi liquid behavior of the model has been confirmed.

AIP conference proceedings•Jan 1, 2020•0 citations

Role of next-nearest-neighbor hopping in thet-t’-Jmodel

Takami Tohyama, Sadamichi Maekawa

A next-nearest-neighbor hopping t' in the t-t'-J model has a different sign between the hole- and electron-doped systems of high-${\mathit{T}}_{\mathit{c}}$ cuprates: t'0 for the hole-doped system and t'>0 for the electron-doped system. We show that the sign is responsible for the remarkable difference of antiferromagnetic (AF) phases between the two systems. To reveal this and clarify the role of t', we examine magnetic excitations of the t-t'-J model by employing exact diagonalization techniques for 4\ifmmode\times\else\texttimes\fi{}4 and \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 lattices. In the low-doping region (two-hole case of the \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 lattice), AF spin correlations are stabilized for the case of t'>0, i.e., electron-doping case, but not for the case of t'0. In the high-doping region (four-hole case of the 4\ifmmode\times\else\texttimes\fi{}4 lattice and more) magnetic excitations are mainly controlled by the geometry of the Fermi surface of the noninteracting system.

Physical review. B, Condensed matter•Feb 1, 1994•167 citations

Effect of Diagonal Hopping and Nearest-Neighbor Coulomb Interaction in Square Hubbard Clusters

Yongzheng Wu, Cong Mei, Yun Liang Gao +2 more

In the high-Tc cuprates, the nanoscale electronic state is important for understanding their com- plex physical properties and unconventional superconducting mechanism. In this work, numerical exact diagonalization method has been used to study the effect of diagonal hopping t' and near- est-neighbor Coulomb interaction V on the electron pair binding energy, spin and charge gaps and corresponding crossover temperatures in the square Hubbard clusters. The calculated results show that t' extends the regime of U in which electron, spin and charge pairings are formed, and corresponding crossover temperature increased. On the contrary, V exhibits opposite effects com- pared to t'. When V approaches to the energy scale of effective attraction induced by U, electron pairing is completely destroyed. Our findings demonstrate that t' can help the formation of super- conducting state, while V will suppress the superconductivity.

•Jan 1, 2015•0 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.

arXiv:2511.13534•Journal of Physics Condensed Matter•Dec 23, 2025•0 citations

Hole motion in thet-Jand Hubbard models: Effect of a next-nearest-neighbor hopping

Eduardo R. Gagliano, Silvia Bacci, Elbio R. Dagotto

Using exact diagonalization techniques, we study one dynamical hole in the two-dimensional t-J and Hubbard models on a square lattice including a next-nearest-neighbor hopping t'. We present the phase diagram in the parameter space (J/t,t'/t), discussing the ground-state properties of the hole. At J=0, a crossing of levels exists at some value of t' separating a ferromagnetic from an antiferromagnetic ground state. For nonzero J, at least four different regions appear where the system behaves like an antiferromagnet or a (not fully saturated) ferromagnet. We study the quasiparticle behavior of the hole, showing that for small values of \ensuremath{\Vert}t'\ensuremath{\Vert} the previously presented string picture is still valid. We also find that, for a realistic set of parameters derived from the Cu-O Hamiltonian, the hole has momentum (\ensuremath{\pi}/2,\ensuremath{\pi}/2), suggesting an enhancement of the p-wave superconducting mode due to the second-neighbor interactions in the spin-bag picture. Results for the t-t'-U model are also discussed with conclusions similar to those of the t-t'-J model. In general we found that t'=0 is not a singular point of these models.

Physical review. B, Condensed matter•Oct 1, 1990•30 citations
The behaviour of high-Tc cuprates in its ground state has been examined within the t-t'-J-J' model using an exact method. The role of next-nearest-neighbor (NNN) hopping (t') and exchange (J') interactions on the charge gap, spin gap and effective exchange interaction has been investigated. Charge gap shows a gapped behavior. Spin gap curves establish a gapless behavior at small t'/t and J'/t. Also, it appears that effective exchange interaction is very much relevant in the present system
The influence of the next-nearest-neighbor (NNN) antiferromagnetic interaction J ’has been examined within t-t'-J-J ’model in an exact technique. An 8-site square cluster is chosen as the representative of the system. The effect of the next-nearest-neighbor (NNN) antiferromagnetic interaction on various ground state properties such as electron-electron correlation, spin-spin correlation, effective hopping amplitude etc. has been studied. Temperature variation of the susceptibility shows that J ’suppresses short range antiferromagnetic order. Applying periodic boundary conditions, the calculations have been extended beyond the 8-site limit.
We present numerical results on the role of next-nearest-neighbor (NNN) Coulomb repulsion within t-J-V-Vʹ model using exact diagonalization (ED) technique within an 8 – site tilted square cluster at a hole doping <h>=0.25. Periodic boundary conditions have been applied to obtain complete basis states. It appears that hole-hole correlation is dominant at d = √2. NNN Coulomb repulsion localizes the electrons and cooperates with exchange interaction J. Non-Fermi liquid behavior of the model has been confirmed.
A next-nearest-neighbor hopping t' in the t-t'-J model has a different sign between the hole- and electron-doped systems of high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates: t'0 for the hole-doped system and t'>0 for the electron-doped system. We show that the sign is responsible for the remarkable difference of antiferromagnetic (AF) phases between the two systems. To reveal this and clarify the role of t', we examine magnetic excitations of the t-t'-J model by employing exact diagonalization techniques for 4\ifmmode\times\else\texttimes\fi{}4 and \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 lattices. In the low-doping region (two-hole case of the \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 lattice), AF spin correlations are stabilized for the case of t'>0, i.e., electron-doping case, but not for the case of t'0. In the high-doping region (four-hole case of the 4\ifmmode\times\else\texttimes\fi{}4 lattice and more) magnetic excitations are mainly controlled by the geometry of the Fermi surface of the noninteracting system.
In the high-Tc cuprates, the nanoscale electronic state is important for understanding their com- plex physical properties and unconventional superconducting mechanism. In this work, numerical exact diagonalization method has been used to study the effect of diagonal hopping t' and near- est-neighbor Coulomb interaction V on the electron pair binding energy, spin and charge gaps and corresponding crossover temperatures in the square Hubbard clusters. The calculated results show that t' extends the regime of U in which electron, spin and charge pairings are formed, and corresponding crossover temperature increased. On the contrary, V exhibits opposite effects com- pared to t'. When V approaches to the energy scale of effective attraction induced by U, electron pairing is completely destroyed. Our findings demonstrate that t' can help the formation of super- conducting state, while V will suppress the superconductivity.
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.
Using exact diagonalization techniques, we study one dynamical hole in the two-dimensional t-J and Hubbard models on a square lattice including a next-nearest-neighbor hopping t'. We present the phase diagram in the parameter space (J/t,t'/t), discussing the ground-state properties of the hole. At J=0, a crossing of levels exists at some value of t' separating a ferromagnetic from an antiferromagnetic ground state. For nonzero J, at least four different regions appear where the system behaves like an antiferromagnet or a (not fully saturated) ferromagnet. We study the quasiparticle behavior of the hole, showing that for small values of \ensuremath{\Vert}t'\ensuremath{\Vert} the previously presented string picture is still valid. We also find that, for a realistic set of parameters derived from the Cu-O Hamiltonian, the hole has momentum (\ensuremath{\pi}/2,\ensuremath{\pi}/2), suggesting an enhancement of the p-wave superconducting mode due to the second-neighbor interactions in the spin-bag picture. Results for the t-t'-U model are also discussed with conclusions similar to those of the t-t'-J model. In general we found that t'=0 is not a singular point of these models.