Absence of the Mott Glass Phase in 1D Disordered Fermionic Systems

We study the competition between the Mott and the Anderson insulating state in a one-dimensional disordered fermionic system. The notorious difficulties associated with strong coupling phases are avoided by using a new description in terms of the kink energies (or instanton surface tension) of the electronic displacement pattern. The approach has some similarities to the description of the flat phase of surfaces undergoing a roughening transition. Tracing back both a finite compressibility and a nonzero ac conductivity to vanishing kink energy we exclude the existence of an intermediate Mott-glass phase in systems with short range interaction only. In systems with long range interaction the Anderson insulating phase exhibits the features of a Mott glass however. The phase diagram is constructed from combining the information from the renormalization group flow, the kink energy, and simple rescaling analysis.

Figure 1

Left: Kink and antikink in the displacement profile $\phi (x)$. The thin lines represent the minima of the potential energy in the absence of the driving force, the bold line one metastable state, and the dashed line the instanton configuration, respectively. Applying a fixed strain to the system, only kinks (or antikinks) are enforced in the system. Right: schematic phase diagram with $w_c\sim {\sigma }^2$.