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arXiv:1803.04426 · Physical review. B./Physical review. B

Mott glass from localization and confinement

Yang-Zhi Chou, Rahul Nandkishore, Leo Radzihovsky

Published May 21, 2018• 9 citations
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Abstract

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.

DOI
10.1103/physrevb.97.184205

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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.
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 investigate the ground-state properties of quantum particles interacting via a long-range repulsive potential ${\mathcal{V}}_{\ensuremath{\sigma}}(x)\ensuremath{\sim}1/|x{|}^{1+\ensuremath{\sigma}}$ ($\ensuremath{-}1<\ensuremath{\sigma}$) or ${\mathcal{V}}_{\ensuremath{\sigma}}(x)\ensuremath{\sim}\ensuremath{-}|x{|}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\sigma}}$ ($\ensuremath{-}2\ensuremath{\le}\ensuremath{\sigma}<\ensuremath{-}1$) that interpolates between the Coulomb potential V0(x){\mathcal{V}}_{0}(x)V0​(x) and the linearly confining potential ${\mathcal{V}}_{\ensuremath{-}2}(x)$ of the Schwinger model. In the absence of disorder the ground state is a Wigner crystal when $\ensuremath{\sigma}\ensuremath{\le}0$. Using bosonization and the nonperturbative functional renormalization group we show that any amount of disorder suppresses the Wigner crystallization when $\ensuremath{-}3/2<\ensuremath{\sigma}\ensuremath{\le}0$; the ground state is then a Mott glass, i.e., a state that has a vanishing compressibility and a gapless optical conductivity. For $\ensuremath{\sigma}<\ensuremath{-}3/2$ the ground state remains a Wigner crystal.