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

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.

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Cited by in corpus (16)

• Anderson localization on random regular graphs
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• Statistics of eigenstates near the localization transition on random regular graphs
• Many-body localization transition with power-law interactions: Statistics of eigenstates
• Multifractality of wave functions on a Cayley tree: From root to leaves
• Eigenstate correlations around many-body localization transition
• Spectral diffusion and scaling of many-body delocalization transitions
• Many-body delocalization transition and relaxation in a quantum dot
• Drude weight fluctuations in many-body localized systems
• Many-body localization in Ising models with random long-range interactions
• Universal short-time dynamics: boundary functional renormalization group for a temperature quench
• Many-body localization of spinless fermions with attractive interactions in one dimension
• Detecting phases in one-dimensional many-fermion systems with the functional renormalization group
• Second order functional renormalization group approach to one-dimensional systems in real and momentum space
• Healing of Defects in Random Antiferromagnetic Spin Chains
• A functional renormalization group approach to electronic structure calculations for systems without translational symmetry