Bound state of a hole and a triplet spin in the $t_1$-$t_2$-$J_1$-$J_2$ model

TL;DR

This paper demonstrates that in certain $t_1$-$t_2$-$J_1$-$J_2$ models, holes and triplet spins form small, mobile bound states that can lead to Bose-Einstein condensation and superconductivity.

Contribution

It reveals the formation of bound states between holes and triplet spins in the $t_1$-$t_2$-$J_1$-$J_2$ model and explores their implications for superconductivity.

Findings

Bound states are spatially small and mobile.

Bound states interact repulsively at short distances.

Finite density of bound states can lead to Bose-Einstein condensation.

Abstract

We show that a hole and a triplet spin form a bound state in a nearly half-filled band of the one- and two-dimensional $t_1$-$t_2$-$J_1$-$J_2$ models. Numerical calculation indicates that the bound state is a spatially small object and moves as a composite particle with spin 1 and charge $+e$ in the spin-gapped background. Two bound states repulsively interact with each other in a short distance and move independently as long as they keep their distance. If a finite density of bound states behave as bosons, the system undergoes the Bose-Einstein condensation which means a superconductivity with charge $+e$.