To shed light into the pairing mechanism of possible spin triplet superconductors ${(\text{TMTSF})}_{2}X$ and ${\text{Sr}}_{2}{\text{RuO}}_{4}$ , we study the competition among various spin singlet and triplet pairing channels in the Hubbard model by calculating the pairing interaction vertex using the ground state quantum Monte Carlo technique. We model ${(\text{TMTSF})}_{2}X$ by a quarter-filled quasi-one-dimensional (quasi-1D) Hubbard model, and the $\ensuremath{\gamma}$ band of ${\text{Sr}}_{2}{\text{RuO}}_{4}$ by a two-dimensional (2D) Hubbard model with a band filling of $\ensuremath{\sim}4∕3$. For the quasi-1D system, we find that triplet $f$ -wave pairing not only dominates over the triplet $p$ wave in agreement with the spin fluctuation theory, but also looks unexpectedly competitive against $d$ waves. For the 2D system, although the results suggest the presence of an attractive interaction in the triplet pairing channels, the $d$ -wave pairing interaction is found to be larger than those of the triplet channels.To shed light into the pairing mechanism of possible spin triplet superconductors ${(\text{TMTSF})}_{2}X$ and ${\text{Sr}}_{2}{\text{RuO}}_{4}$, we study the competition among various spin singlet and triplet pairing channels in the Hubbard model by calculating the pairing interaction vertex using the ground state quantum Monte Carlo technique. We model ${(\text{TMTSF})}_{2}X$ by a quarter-filled quasi-one-dimensional (quasi-1D) Hubbard model, and the $\ensuremath{\gamma}$ band of ${\text{Sr}}_{2}{\text{RuO}}_{4}$ by a two-dimensional (2D) Hubbard model with a band filling of $\ensuremath{\sim}4∕3$. For the quasi-1D system, we find that triplet $f$-wave pairing not only dominates over the triplet $p$ wave in agreement with the spin fluctuation theory, but also looks unexpectedly competitive against $d$ waves. For the 2D system, although the results suggest the presence of an attractive interaction in the triplet pairing channels, the $d$-wave pairing interaction is found to be larger than those of the triplet channels.

arXiv:cond-mat/0307553Physical Review BJun 18, 200431 citations

The Pairing Interaction in the 2D Hubbard Model

Thomas Maier, Mark Jarrell, Douglas J. Scalapino

A dynamic cluster quantum Monte Carlo approximation is used to study the effective pairing interaction of a 2D Hubbard model with a near neighbor hopping $t$ and an on-site Coulomb interaction $U$ . The effective pairing interaction is characterized in terms of the momentum and frequency dependence of the eigenfunction of the leading eigenvalue of the irreducible particle-particle vertex. The momentum dependence of this eigenfunction is found to vary as $(\cos k_x-\cos k_y)$ over most of the Brillouin zone and its frequency dependence is determined by the exchange energy $J$ . This implies that the effective pairing interaction is attractive for singlets formed between near-neighbor sites and retarded on a time scale set by $J^{-1}$ . The strength of the pairing interaction measured by the size of the d-wave eigenvalue peaks for $U$ of order the bandwidth $8t$ . It is found to increase as the system is underdoped.A dynamic cluster quantum Monte Carlo approximation is used to study the effective pairing interaction of a 2D Hubbard model with a near neighbor hopping $t$ and an on-site Coulomb interaction $U$ . The effective pairing interaction is characterized in terms of the momentum and frequency dependence of the eigenfunction of the leading eigenvalue of the irreducible particle-particle vertex. The momentum dependence of this eigenfunction is found to vary as $(\cos k_x-\cos k_y)$ over most of the Brillouin zone and its frequency dependence is determined by the exchange energy $J$. This implies that the effective pairing interaction is attractive for singlets formed between near-neighbor sites and retarded on a time scale set by $J^{-1}$. The strength of the pairing interaction measured by the size of the d-wave eigenvalue peaks for $U$ of order the bandwidth $8t$. It is found to increase as the system is underdoped.

arXiv:cond-mat/0606003May 31, 20060 citations

To shed light into the pairing mechanism of possible spin triplet superconductors

{(\text{TMTSF})}_{2}X

and

{\text{Sr}}_{2}{\text{RuO}}_{4}

, we study the competition among various spin singlet and triplet pairing channels in the Hubbard model by calculating the pairing interaction vertex using the ground state quantum Monte Carlo technique. We model

{(\text{TMTSF})}_{2}X

by a quarter-filled quasi-one-dimensional (quasi-1D) Hubbard model, and the $\ensuremath{\gamma}$ band of

{\text{Sr}}_{2}{\text{RuO}}_{4}

by a two-dimensional (2D) Hubbard model with a band filling of $\ensuremath{\sim}4∕3$. For the quasi-1D system, we find that triplet

f

-wave pairing not only dominates over the triplet

p

wave in agreement with the spin fluctuation theory, but also looks unexpectedly competitive against

d

waves. For the 2D system, although the results suggest the presence of an attractive interaction in the triplet pairing channels, the

d

-wave pairing interaction is found to be larger than those of the triplet channels.

A dynamic cluster quantum Monte Carlo approximation is used to study the effective pairing interaction of a 2D Hubbard model with a near neighbor hopping

t

and an on-site Coulomb interaction

U

. The effective pairing interaction is characterized in terms of the momentum and frequency dependence of the eigenfunction of the leading eigenvalue of the irreducible particle-particle vertex. The momentum dependence of this eigenfunction is found to vary as

(\cos k_x-\cos k_y)

over most of the Brillouin zone and its frequency dependence is determined by the exchange energy

J

. This implies that the effective pairing interaction is attractive for singlets formed between near-neighbor sites and retarded on a time scale set by

J^{-1}

. The strength of the pairing interaction measured by the size of the d-wave eigenvalue peaks for

U

of order the bandwidth

8t

. It is found to increase as the system is underdoped.