Numerical study of a superconductor-insulator transition in a half-filled Hubbard chain with distant transfers

TL;DR

This study uses numerical methods to investigate a one-dimensional Hubbard model with next-nearest neighbor hopping, revealing a transition from a superconducting to an insulating state as interaction strength increases.

Contribution

It provides a numerical validation of the superconductor-insulator transition in a Hubbard chain with distant transfers, supporting recent weak-coupling theories.

Findings

Pairing correlations decay slowly at moderate U

Insulating behavior emerges for U > U_C~3t

Transition aligns with weak-coupling theory predictions

Abstract

The ground state of a one-dimensional Hubbard model having the next-nearest neighbor hopping (t') as well as the nearest-neighbor one (t) is numerically investigated at half-filling. A quantum Monte Carlo result shows a slowly decaying pairing correlation for a sizeable interaction strength $(U \leq 2t)$, while the system is shown to become insulating for yet larger $U>U_C\sim 3t$ from a direct evaluation of the charge gap with the density-matrix renormalization group method. The results are consistent with Fabrizio's recent weak-coupling theory which suggests a transition from a superconductor into an insulator at a finite U.