Disorder-induced phase transitions in a spinful one-dimensional system

Abstract

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 ν=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.