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arXiv:2007.02993 · Physical Review Letters

Mott-Glass Phase of a One-Dimensional Quantum Fluid with Long-Range Interactions

Romain Daviet, N. Dupuis

Published Dec 2, 2020• 16 citations
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Abstract

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 ${\mathcal{V}}_{0}(x)$ 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.

DOI
10.1103/physrevlett.125.235301

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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 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 one-dimensional disordered Bose fluid using bosonization, the replica method, and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale k, quantum tunneling between the ground state and low-lying metastable states leads to a rounding of the cusp singularity into a quantum boundary layer (QBL). The width of the QBL depends on an effective Luttinger parameter K_{k}∼k^{θ} that vanishes with an exponent θ=z-1 related to the dynamical critical exponent z. The QBL encodes the existence of rare "superfluid" regions, controls the low-energy dynamics, and yields a (dissipative) conductivity vanishing as ω^{2} in the low-frequency limit. These results reveal the glassy properties (pinning, "shocks," or static avalanches) of the Bose-glass phase and can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.
We study the superfluid--Bose-glass transition in a one-dimensional lattice boson model with power-law decaying hopping amplitude ${t}_{i\ensuremath{-}j}\ensuremath{\sim}1/{|i\ensuremath{-}j|}^{\ensuremath{\alpha}}$, using bosonization and the nonperturbative functional renormalization group (FRG). When $\ensuremath{\alpha}$ is smaller than a critical value ${\ensuremath{\alpha}}_{c}<3$, the U(1) symmetry is spontaneously broken, which leads to a density mode with nonlinear dispersion and dynamical exponent $z=(\ensuremath{\alpha}\ensuremath{-}1)/2$; the superfluid phase is then stable for sufficiently weak disorder, contrary to the case of short-range hopping where disorder is a relevant perturbation when the Luttinger parameter is smaller than 3/23/23/2. In the presence of disorder, however, long-range hopping has no effect in the infrared limit and the FRG flow eventually becomes similar to that of a boson system with short-range hopping. This implies that the superfluid phase, when stable, exhibits a density mode with linear dispersion (z=1z=1z=1) and the superfluid--Bose-glass transition remains in the Berezinskii-Kosterlitz-Thouless universality class, while the Bose-glass fixed point is insensitive to long-range hopping. We compare our findings with a recent numerical study.