The Hubbard model on a square lattice is one of the most studied condensed-matter quantum problems.Here we find evidence that for intermediate $U/4t$ values and a hole-concentration range $x\in (x_c,x_*)$ the ground state of the Hubbard model on the square lattice perturbed by weak three-dimensional (3D) uniaxial anisotropy has long-range d-wave superconducting order. Here $t$ is the effective nearest-neighbor transfer integral and $U$ the effective on-site repulsion. The lower critical concentration $x_c$ involves the Ginzburg number Gi and is approximately given by $x_c\approx {\rm Gi}+x_0\approx 0.05$ . Here $x_0The Hubbard model on a square lattice is one of the most studied condensed-matter quantum problems.Here we find evidence that for intermediate $U/4t$ values and a hole-concentration range $x\in (x_c,x_*)$ the ground state of the Hubbard model on the square lattice perturbed by weak three-dimensional (3D) uniaxial anisotropy has long-range d-wave superconducting order. Here $t$ is the effective nearest-neighbor transfer integral and $U$ the effective on-site repulsion. The lower critical concentration $x_c$ involves the Ginzburg number Gi and is approximately given by $x_c\approx {\rm Gi}+x_0\approx 0.05$. Here $x_0

arXiv:0804.2388Apr 15, 20080 citations

Superconductivity in the Repulsive Hubbard Model

D. Baeriswyl

Journal of Superconductivity and Novel MagnetismDec 21, 201015 citations

A $B_{1g}$ phonon unlocks $d$ -wave superconductivity in the repulsive Hubbard modelA $B_{1g}$ phonon unlocks $d$-wave superconductivity in the repulsive Hubbard model

Wen O. Wang, Tianshu Li, Xiaoyue Ma +9 more

Using numerically exact finite-temperature quantum Monte Carlo, we demonstrate that a $B_{1g}$ phonon coupled to the doped $t$ - $t'$ repulsive Hubbard model produces genuine $d$ -wave superconductivity at a substantial transition temperature, in excess of either interaction alone. The observed trends suggest that stronger Hubbard repulsion may cooperate with the phonon to further raise the pairing scale. The enhancement persists at stronger repulsion within the accessible window, limited by the fermion sign problem, and follows a common trend across phonon frequencies $Ω$ when organized by a retardation scale $2πT/Ω$ . We also find a well-defined superconducting dome in doping, echoing a characteristic feature of correlated superconductors. Our results identify the $B_{1g}$ phonon as a plausible microscopic ingredient for robust $d$ -wave superconductivity in the Hubbard model and suggest a concrete, physically motivated route toward materials with higher superconducting transition temperatures.Using numerically exact finite-temperature quantum Monte Carlo, we demonstrate that a $B_{1g}$ phonon coupled to the doped $t$-$t'$ repulsive Hubbard model produces genuine $d$-wave superconductivity at a substantial transition temperature, in excess of either interaction alone. The observed trends suggest that stronger Hubbard repulsion may cooperate with the phonon to further raise the pairing scale. The enhancement persists at stronger repulsion within the accessible window, limited by the fermion sign problem, and follows a common trend across phonon frequencies $Ω$ when organized by a retardation scale $2πT/Ω$. We also find a well-defined superconducting dome in doping, echoing a characteristic feature of correlated superconductors. Our results identify the $B_{1g}$ phonon as a plausible microscopic ingredient for robust $d$-wave superconductivity in the Hubbard model and suggest a concrete, physically motivated route toward materials with higher superconducting transition temperatures.

arXiv:2610.37746Oct 27, 20260 citations

Inhomogeneity and d-wave superconductivity in the Hubbard model

Shiladitya Chakraborty, David Sénéchal, A.–M. S. Tremblay

Bulletin of the American Physical SocietyMar 24, 20110 citations

Density matrix renormalization group study of superconductivity in the triangular lattice Hubbard model

Jordan Venderley, Eun-Ah Kim

With the discovery of strong-coupling physics and superconductivity in moir\'e superlattices, it is essential to have an understanding of strong-coupling driven superconductivity in systems with trigonal symmetry. The simplest lattice model with trigonal symmetry is the triangular lattice Hubbard model. Although the triangular lattice spin model is a heavily studied model in the context of frustration, studies of the hole-doped triangular lattice Hubbard model are rare. Here, we use density matrix renormalization group to investigate the dominant superconducting channels in the hole-doped triangular lattice Hubbard model over a range of repulsive interaction strengths. We find a clear transition from $p$ -wave superconductivity at a moderate on-site repulsion strength ( $U/t=2$ ) at filling above 1/4 ($n\ensuremath{\sim}0.65$) to $d$ -wave superconductivity at a strong on-site repulsion strength ( $U/t=10$ ) at filling below 1/4 ($n\ensuremath{\sim}0.4$). The unusual tunability that moir\'e superlattices offer in controlling $U/t$ would open up the opportunity to realize this transition between $d$ -wave and $p$ -wave superconductivity.With the discovery of strong-coupling physics and superconductivity in moir\'e superlattices, it is essential to have an understanding of strong-coupling driven superconductivity in systems with trigonal symmetry. The simplest lattice model with trigonal symmetry is the triangular lattice Hubbard model. Although the triangular lattice spin model is a heavily studied model in the context of frustration, studies of the hole-doped triangular lattice Hubbard model are rare. Here, we use density matrix renormalization group to investigate the dominant superconducting channels in the hole-doped triangular lattice Hubbard model over a range of repulsive interaction strengths. We find a clear transition from $p$-wave superconductivity at a moderate on-site repulsion strength ($U/t=2$) at filling above 1/4 ($n\ensuremath{\sim}0.65$) to $d$-wave superconductivity at a strong on-site repulsion strength ($U/t=10$) at filling below 1/4 ($n\ensuremath{\sim}0.4$). The unusual tunability that moir\'e superlattices offer in controlling $U/t$ would open up the opportunity to realize this transition between $d$-wave and $p$-wave superconductivity.

arXiv:1901.11034Physical review. B./Physical review. BAug 26, 201938 citations

Superconductivity in the Hubbard model with repulsion

R. O. Zaǐtsev, В. А. Иванов

Aug 1, 19870 citations

The Hubbard model on a square lattice is one of the most studied condensed-matter quantum problems.Here we find evidence that for intermediate

U/4t

values and a hole-concentration range

x\in (x_c,x_*)

the ground state of the Hubbard model on the square lattice perturbed by weak three-dimensional (3D) uniaxial anisotropy has long-range d-wave superconducting order. Here

t

is the effective nearest-neighbor transfer integral and

U

the effective on-site repulsion. The lower critical concentration

x_c

involves the Ginzburg number Gi and is approximately given by

x_c\approx {\rm Gi}+x_0\approx 0.05

. Here $x_0

B_{1g}

phonon unlocks

d

-wave superconductivity in the repulsive Hubbard model

Using numerically exact finite-temperature quantum Monte Carlo, we demonstrate that a

B_{1g}

phonon coupled to the doped

t

t'

repulsive Hubbard model produces genuine

d

-wave superconductivity at a substantial transition temperature, in excess of either interaction alone. The observed trends suggest that stronger Hubbard repulsion may cooperate with the phonon to further raise the pairing scale. The enhancement persists at stronger repulsion within the accessible window, limited by the fermion sign problem, and follows a common trend across phonon frequencies

Ω

when organized by a retardation scale

2πT/Ω

. We also find a well-defined superconducting dome in doping, echoing a characteristic feature of correlated superconductors. Our results identify the

B_{1g}

phonon as a plausible microscopic ingredient for robust

d

-wave superconductivity in the Hubbard model and suggest a concrete, physically motivated route toward materials with higher superconducting transition temperatures.

p

-wave superconductivity at a moderate on-site repulsion strength (

U/t=2

) at filling above 1/4 ($n\ensuremath{\sim}0.65$) to

d

-wave superconductivity at a strong on-site repulsion strength (

U/t=10

) at filling below 1/4 ($n\ensuremath{\sim}0.4$). The unusual tunability that moir\'e superlattices offer in controlling

U/t

would open up the opportunity to realize this transition between

d

-wave and

p

-wave superconductivity.