Approaching Many-Body Localization from Disordered Luttinger Liquids via the Functional Renormalization Group

TL;DR

This paper investigates how interactions and disorder influence transport in one-dimensional fermion systems, using the functional renormalization group and matrix product states to analyze conductance behavior and scaling, advancing understanding of many-body localization.

Contribution

It applies the functional renormalization group to study disordered Luttinger liquids, providing new insights into conductance scaling and non-ohmic behavior in large systems.

Findings

Identification of non-ohmic power law regimes in conductance

Demonstration of universal single-parameter conductance scaling

Validation of FRG results with matrix product state benchmarks

Abstract

We study the interplay of interactions and disorder in a one-dimensional fermion lattice coupled adiabatically to infinite reservoirs. We employ both the functional renormalization group (FRG) as well as matrix product state techniques, which serve as an accurate benchmark for small systems. Using the FRG, we compute the length- and temperature-dependence of the conductance averaged over $10^4$ samples for lattices as large as $10^{5}$ sites. We identify regimes in which non-ohmic power law behavior can be observed and demonstrate that the corresponding exponents can be understood by adapting earlier predictions obtained perturbatively for disordered Luttinger liquids. In presence of both disorder and isolated impurities, the conductance has a universal single-parameter scaling form. This lays the groundwork for an application of the functional renormalization group to the realm of many-body localization.