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arXiv:cond-mat/0701114 · Physical Review Letters

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

Thomas Nattermann, Aleksandra Petković, Zoran Ristivojević, Friedmar Schütze

Published Oct 31, 2007• 9 citations
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Abstract

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.

DOI
10.1103/physrevlett.99.186402

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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.
We study the competition between a random potential and a commensurate potential on interacting fermionic and bosonic systems using a variety of methods. We focus on one-dimensional interacting fermionic systems, but higher-dimensional bosonic and fermionic extensions, as well as classical equivalents, are also discussed. Our methods, which include the bosonization method, the replica variational method, the functional renormalization group method, and perturbation around the atomic limit, go beyond conventional perturbative expansions around the Luttinger liquid in one dimension. All these methods agree on the prediction in these systems of a phase, the Mott glass, intermediate between the Anderson (compressible, with a pseudogap in the optical conductivity) and the Mott (incompressible with a gap in the optical conductivity) insulator. The Mott glass, which was unexpected from a perturbative renormalization-group point of view has a pseudogap in the conductivity while remaining incompressible. Having derived the existence of a Mott glass phase in one dimension, we show qualitatively that its existence can also be expected in higher dimensions. We discuss the relevance of this phase to experimental systems such as disordered classical elastic systems and dirty bosons.
We study a system of fermions in one spatial dimension with linearly confining interactions and short-range disorder. We focus on the zero-temperature properties of this system, which we characterize using bosonization and the Gaussian variational method. We compute the static compressibility and ac conductivity, and thereby demonstrate that the system is incompressible, but exhibits gapless optical conductivity. This corresponds to a ``Mott glass'' state, distinct from an Anderson and a fully gapped Mott insulator, arising due to the interplay of disorder and charge confinement. We argue that this Mott glass phenomenology should persist to nonzero temperatures.
We study a one-dimensional disordered quantum fluid with linearly confining interactions (disordered Schwinger model) using bosonization and the nonperturbative functional renormalization group. We find that the long-range interactions make the Anderson-insulator (or, for bosons, the Bose-glass) fixed point (corresponding to a compressible state with a gapless optical conductivity) unstable, even if the latter may control the flow at intermediate energy scales. The stable fixed point describes an incompressible ground state with a gapped optical conductivity similar to a Mott insulator. These results disagree with the Gaussian variational method that predicts a Mott glass, namely a state with vanishing compressibility but a gapless optical conductivity.
Dielectric responces of the one-dimentional electron system is investigated numerically. We treat an interacting one-dimentional spinless fermion model with disorder by using the Density Matrix Renormalization Group(DMRG) method which is extended for nonuniform systems. We apply an electric field EEE to the system and calculate dielectric responces. Dielectric responce of the Mott insulator and the Anderson insulator are calculated respectively. Steplike behaviors in P−EP-EP−E curve are obtained which corresponds to breakdown of the insulating behavior. For the Mott insulator, the steps originate from generation of kink-pairs. For the Anderson insulator on the other hand, the origin of the steps is a crossing of the localized one particle energy levels. We also treat random systems with interaction. From one parameter scaling analysis of the susceptibility χχχ, the metal-insulator transition in attractively interacting region is confirmed and a phase diagram of the random spinless fermion model is obtained.