Spin Gap of the One-Dimensional t-J-J′ Model

Abstract

We investigate the one-dimensional t-J-J′ model by the numerical diagonalization where a few holes are doped in the half-filled band. By introducing a finite-size scaling, we estimate the spin gap at J′⁄J=0.5 and J⁄t=2. When one hole is doped, the spin gap decreases to 0.190J in comparison with 0.236J which is the spin gap of the half-filled band. The spin gap further reduces to 0.141J for two-hole doping and to about 0.05J for three-hole doping. This result shows that the value of the spin gap as a function of the electron density is discontinuous at half-filling.