Monte Carlo study of the pairing interaction in the two-leg Hubbard ladder

TL;DR

This study uses Monte Carlo simulations to analyze pairing interactions in a doped two-leg Hubbard ladder, revealing magnetic correlations and $d_{x^2-y^2}$ pairing symmetry at low temperatures.

Contribution

It provides new insights into the momentum-space structure of pairing interactions and the conditions favoring pairing in the Hubbard ladder model.

Findings

Interaction develops structure similar to magnetic susceptibility as temperature lowers

Leading eigenfunction shows $d_{x^2-y^2}$ symmetry

Spectral weight peaks near $(\pi,0)$ and $(0,\pi)$ for certain hopping ratios

Abstract

Monte Carlo calculations of the irreducible particle-particle interaction on a two-leg Hubbard ladder doped near half-filling are reported. As the temperature is lowered, this interaction develops structure in momentum space similar to the magnetic susceptibility $\chi(q)$ and reflects the development of strong short-range antiferromagnetic correlations. Using this interaction, the eigenfunction of the leading singlet pair eigenvalue is found to have $d_{x^2-y^2}$ like symmetry. The single-particle spectral weight is also shown to peak near $(\pi,0)$ and $(0,\pi)$ when the ratio of the inter- to intra-chain hopping $t_{\perp}/t\simeq 1.5$, leading to an increased tendency for pairing.