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/0508639 · Physical Review B

Crossover from d -wave to p -wave pairing in the t−t′ Hubbard model at zero temperature

Ryotaro Arita, Karsten Held

Published Feb 22, 2006• 7 citations
arXivHTMLPDF

Abstract

We develop an algorithm which employs the projective quantum Monte Carlo method for solving the equations of the dynamical cluster approximation at zero temperature, and apply it for studying pair susceptibilities of the two-dimensional Hubbard-model with next-nearest neighbor hopping. In particular, we identify which pairing symmetry is dominant in the $U\ensuremath{-}n$ parameter space ($U$: repulsive Coulomb interaction; $n$: electron density). We find that ${p}_{x+{y}^{\ensuremath{-}}}({d}_{{x}^{2}\ensuremath{-}{y}^{2\ensuremath{-}}})$ wave is dominant among triplet (singlet) pairings---at least for $0.3<n<0.8$ and $U\ensuremath{\leqslant}4t$. The crossover between ${d}_{{x}^{2}\ensuremath{-}{y}^{2\ensuremath{-}}}$ wave and ${p}_{x+{y}^{\ensuremath{-}}}$ wave occurs around $n\ensuremath{\sim}0.4$.

DOI
10.1103/physrevb.73.064515

Related papers

Quantum Monte Carlo study of the Hubbard model with next-nearest-neighbor hopping t ′: pairing and magnetism

Shuhui Yang, Tao Ying, Weiqi Li +3 more

Using the finite-temperature determinant quantum Monte Carlo (DQMC) algorithm, we study the pairing symmetries of the Hubbard Hamiltonian with next-nearest-neighbor (NNN) hopping t' on square lattices. By varying the value of t', we find that the d-wave pairing is suppressed by the onset of t', while the p + ip-wave pairing tends to emerge for low electron density and t' around -0.7. Together with the calculation of the anti-ferromagnetic and ferromagnetic spin correlation function, we explore the relationship between anti-ferromagnetic order and the d-wave pairing symmetry, and the relationship between ferromagnetic order and the p + ip-wave pairing symmetry. Our results may be useful for the exploration of the mechanism of the electron pairing symmetries, and for the realization of the exotic p + ip-wave superconductivity.

Journal of Physics Condensed Matter•Dec 14, 2020•9 citations

Study of d- and p-wave Pairing in the Hubbard Model Using the Dynamical Cluster Approximation

Ryotaro Arita, Karsten Held

The Hubbard model is commonly considered to be relevant for unconventional superconductors like cuprates and ruthenates. For a more thorough insight into the physics of this model, we use a new projective quantum Monte Carlo (PQMC) algorithm within the framework of the dynamical cluster approximation (DCA). Employing this DCA(PQMC) approach, we calculate static pairing susceptibilities for various symmetries and study the crossover from dx2−y2‐wave to px+y‐wave pairing as a function of doping.

AIP conference proceedings•Jan 1, 2006•0 citations

Spin-triplet pairing instability in a two-dimensional repulsive Hubbard model

X. Liu, Yu-Feng Song, Yuan-Yao He +2 more

The search for superconductivity with unconventional pairing symmetry has been a central focus in the study of strongly correlated electron systems. In this work, we report a numerically exact study of the spin-triplet pairing in a two-dimensional Hubbard model with repulsive interactions, employing the determinant quantum Monte Carlo method. The model includes next-nearest-neighbor and third-nearest-neighbor hopping terms and maintains spin balance. By tuning the fermion filling close to a type-II Van Hove singularity (VHS) in the model, we numerically investigate the ordering tendencies of several possible pairing channels with different symmetries. Our numerical results provide clear evidence of the spin-triplet $p$-wave pairing instability approaching low temperatures, as revealed by the vertex contribution to the pairing susceptibility. This signature becomes increasingly pronounced as the interaction strength increases in the weak to intermediate regime. We further find that, near the type-II VHS, the dominant spin-spin correlations in the system are ferromagnetic, suggesting its close relation to the spin-triplet pairing instability. Our findings offer a reliable approach to realize spin-triplet $p$-wave superfluidity in the repulsive Hubbard model from an unbiased numerical perspective.

arXiv:2507.09295•Physical Review A•Nov 21, 2025•0 citations

Lifshitz transition in the two-dimensional Hubbard model

K.-S. Chen, Zi Yang Meng, Thomas Pruschke +2 more

Using large-scale dynamical cluster quantum Monte Carlo simulations, we study the Lifshitz transition of the two-dimensional Hubbard model with next-nearest-neighbor hopping (${t}^{\ensuremath{'}}$), chemical potential, and temperature as control parameters. At ${t}^{\ensuremath{'}}\ensuremath{\le}0$, we identify a line of Lifshitz transition points associated with a change in the Fermi surface topology at zero temperature. In the overdoped region, the Fermi surface is complete and electron-like; across the Lifshitz transition, the Fermi surface becomes hole-like and develops a pseudogap. At (or very close to) the Lifshitz transition points, a van Hove singularity in the density of states crosses the Fermi level. The van Hove singularity occurs at finite doping due to correlation effects and becomes more singular when ${t}^{\ensuremath{'}}$ becomes more negative. The resulting temperature dependence on the bare $d$-wave pairing susceptibility close to the Lifshitz points is significantly different from that found in the traditional van Hove scenarios. Such unambiguous numerical observation of the Lifshitz transition at ${t}^{\ensuremath{'}}\ensuremath{\le}0$ extends our understanding of the quantum critical region in the phase diagram and shines lights on future investigations of the nature of the quantum critical point in the two-dimensional Hubbard model.

arXiv:1207.0796•Physical Review B•Oct 31, 2012•52 citations

Enhanced pairing in the repulsive Hubbard model with next-nearest-neighbor hopping

Raimundo R. dos Santos

We study the behavior of pair susceptibilities in the two-dimensional repulsive Hubbard model with next-nearest-neighbor hopping ${t}_{2}$ by Monte Carlo simulations. In a certain range of band filling, we find that the d-wave pair susceptibilities can be enhanced by a Hubbard repulsion U with respect to the noninteracting case, unlike the case with ${t}_{2}$=0. We discuss the connection of this model to ${\mathrm{CuO}}_{2}$ planes in the oxide superconductors and the possible implication of our results for these materials.

Physical review. B, Condensed matter•Apr 1, 1989•28 citations

d -wave superconductivity in the presence of nearest-neighbor Coulomb repulsion

Mi Jiang, Urs R. Hähner, T. C. Schulthess +1 more

Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of $d$-wave pairing when a nearest-neighbor Coulomb repulsion $V$ is present in addition to the on-site Coulomb repulsion $U$. We find that $d$-wave pairing and the superconducting transition temperature ${T}_{c}$ are only weakly suppressed as long as $V$ does not exceed $U/2$. This stability is traced to the strongly retarded nature of pairing that allows the $d$-wave pairs to minimize the repulsive effect of $V$. When $V$ approaches $U/2$, large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of $d$-wave pairing and ${T}_{c}$ than for smaller $V$.

arXiv:1707.06093•Physical review. B./Physical review. B•May 17, 2018•31 citations
We develop an algorithm which employs the projective quantum Monte Carlo method for solving the equations of the dynamical cluster approximation at zero temperature, and apply it for studying pair susceptibilities of the two-dimensional Hubbard-model with next-nearest neighbor hopping. In particular, we identify which pairing symmetry is dominant in the U\ensuremath−nU\ensuremath{-}nU\ensuremath−n parameter space (UUU: repulsive Coulomb interaction; nnn: electron density). We find that px+y\ensuremath−(dx2\ensuremath−y2\ensuremath−){p}_{x+{y}^{\ensuremath{-}}}({d}_{{x}^{2}\ensuremath{-}{y}^{2\ensuremath{-}}})px+y\ensuremath−​(dx2\ensuremath−y2\ensuremath−​) wave is dominant among triplet (singlet) pairings---at least for 0.3<n<0.80.3<n<0.80.3<n<0.8 and U\ensuremath⩽4tU\ensuremath{\leqslant}4tU\ensuremath⩽4t. The crossover between dx2\ensuremath−y2\ensuremath−{d}_{{x}^{2}\ensuremath{-}{y}^{2\ensuremath{-}}}dx2\ensuremath−y2\ensuremath−​ wave and px+y\ensuremath−{p}_{x+{y}^{\ensuremath{-}}}px+y\ensuremath−​ wave occurs around n\ensuremath∼0.4n\ensuremath{\sim}0.4n\ensuremath∼0.4.
Using the finite-temperature determinant quantum Monte Carlo (DQMC) algorithm, we study the pairing symmetries of the Hubbard Hamiltonian with next-nearest-neighbor (NNN) hopping t' on square lattices. By varying the value of t', we find that the d-wave pairing is suppressed by the onset of t', while the p + ip-wave pairing tends to emerge for low electron density and t' around -0.7. Together with the calculation of the anti-ferromagnetic and ferromagnetic spin correlation function, we explore the relationship between anti-ferromagnetic order and the d-wave pairing symmetry, and the relationship between ferromagnetic order and the p + ip-wave pairing symmetry. Our results may be useful for the exploration of the mechanism of the electron pairing symmetries, and for the realization of the exotic p + ip-wave superconductivity.
The Hubbard model is commonly considered to be relevant for unconventional superconductors like cuprates and ruthenates. For a more thorough insight into the physics of this model, we use a new projective quantum Monte Carlo (PQMC) algorithm within the framework of the dynamical cluster approximation (DCA). Employing this DCA(PQMC) approach, we calculate static pairing susceptibilities for various symmetries and study the crossover from dx2−y2‐wave to px+y‐wave pairing as a function of doping.
The search for superconductivity with unconventional pairing symmetry has been a central focus in the study of strongly correlated electron systems. In this work, we report a numerically exact study of the spin-triplet pairing in a two-dimensional Hubbard model with repulsive interactions, employing the determinant quantum Monte Carlo method. The model includes next-nearest-neighbor and third-nearest-neighbor hopping terms and maintains spin balance. By tuning the fermion filling close to a type-II Van Hove singularity (VHS) in the model, we numerically investigate the ordering tendencies of several possible pairing channels with different symmetries. Our numerical results provide clear evidence of the spin-triplet ppp-wave pairing instability approaching low temperatures, as revealed by the vertex contribution to the pairing susceptibility. This signature becomes increasingly pronounced as the interaction strength increases in the weak to intermediate regime. We further find that, near the type-II VHS, the dominant spin-spin correlations in the system are ferromagnetic, suggesting its close relation to the spin-triplet pairing instability. Our findings offer a reliable approach to realize spin-triplet ppp-wave superfluidity in the repulsive Hubbard model from an unbiased numerical perspective.
Using large-scale dynamical cluster quantum Monte Carlo simulations, we study the Lifshitz transition of the two-dimensional Hubbard model with next-nearest-neighbor hopping (${t}^{\ensuremath{'}}$), chemical potential, and temperature as control parameters. At ${t}^{\ensuremath{'}}\ensuremath{\le}0$, we identify a line of Lifshitz transition points associated with a change in the Fermi surface topology at zero temperature. In the overdoped region, the Fermi surface is complete and electron-like; across the Lifshitz transition, the Fermi surface becomes hole-like and develops a pseudogap. At (or very close to) the Lifshitz transition points, a van Hove singularity in the density of states crosses the Fermi level. The van Hove singularity occurs at finite doping due to correlation effects and becomes more singular when ${t}^{\ensuremath{'}}$ becomes more negative. The resulting temperature dependence on the bare ddd-wave pairing susceptibility close to the Lifshitz points is significantly different from that found in the traditional van Hove scenarios. Such unambiguous numerical observation of the Lifshitz transition at ${t}^{\ensuremath{'}}\ensuremath{\le}0$ extends our understanding of the quantum critical region in the phase diagram and shines lights on future investigations of the nature of the quantum critical point in the two-dimensional Hubbard model.
We study the behavior of pair susceptibilities in the two-dimensional repulsive Hubbard model with next-nearest-neighbor hopping t2{t}_{2}t2​ by Monte Carlo simulations. In a certain range of band filling, we find that the d-wave pair susceptibilities can be enhanced by a Hubbard repulsion U with respect to the noninteracting case, unlike the case with t2{t}_{2}t2​=0. We discuss the connection of this model to CuO2{\mathrm{CuO}}_{2}CuO2​ planes in the oxide superconductors and the possible implication of our results for these materials.
Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of ddd-wave pairing when a nearest-neighbor Coulomb repulsion VVV is present in addition to the on-site Coulomb repulsion UUU. We find that ddd-wave pairing and the superconducting transition temperature Tc{T}_{c}Tc​ are only weakly suppressed as long as VVV does not exceed U/2U/2U/2. This stability is traced to the strongly retarded nature of pairing that allows the ddd-wave pairs to minimize the repulsive effect of VVV. When VVV approaches U/2U/2U/2, large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of ddd-wave pairing and Tc{T}_{c}Tc​ than for smaller VVV.