Spin-gap phase in the extended t-J chain

Abstract

We study the one-dimensional deformed $t-t^{\prime}-J$ model in terms of the continuum field theories. We found that at low doping concentration and far away from the phase separation regime, there are two phases: the Luttinger liquid and the Luther-Emery liquid, depending on t&#39;/t<(t&#39;/t)_c or t&#39;/t>(t&#39;/t)_c, where (t&#39;/t)_c>0. Moreover, the singlet superconducting correlations are dominant in the Luther-Emery liquid.