We analyse a modified set of renormalisation group equations for disordered spinful fermions described by the Luttinger liquid model. The modification is necessary to take special care of the factitious admixture of the disorder to the interaction coupling constants undergoing renormalisation. Only properly separated amplitudes of elastic and inelastic processes allow the identification of true phases and the construction of the phase diagram (a similar procedure has been earlier implemented for the spinless case). In the spinful case, these modified equations enable us to demonstrate that in some region of the bare parameters values the phase diagram contains two massive phases, charge (CDW) and spin (SDW) density waves, which are separated by an insulating phase. These gapped phases are achieved at finite critical temperatures that vanish at the phase boundaries indicating the presence of a disorder-induced quantum phase transition. The critical temperatures as a function of disorder are reasonably well fit by a stretch exponential with the universal stretching critical exponent $\nu =1∕3$. A quantum phase transition between CDW and SDW phases driven by disorder strength has not been predicted before and this observation must be taken into account when analysing recent multiple experiments on phase transitions in quasi-one-dimensional structures.

我们分析了由Luttinger液体模型描述的无序棘形费米子的一组修正的重整化组方程。该修饰对于特殊照顾该疾病与正经历重新规范化的相互作用耦合常数的人为混合是必要的。只有将弹性和非弹性过程的振幅适当地分开，才能识别真实的相位并构造相图（较早地针对无旋转情况已经执行了类似的过程）。在多刺的情况下，这些修改后的方程式使我们能够证明，在裸参数值的某些区域中，相图包含两个块状相，即电荷（CDW）和自旋（SDW）密度波，它们被一个绝缘相隔开。这些间隙相在有限的临界温度下实现，该临界温度在相界处消失，表明存在无序诱导的量子相变。临界温度作为无序的函数，可以通过拉伸指数与通用拉伸临界指数很好地拟合$\nu =\mathrm{1个}∕3$。以前从未预测过由无序强度驱动的CDW和SDW相之间的量子相变，在分析最近关于准一维结构的相变的多个实验时，必须考虑到这一观察结果。