Density Propagator for Many-Body Localization: Finite-Size Effects, Transient Subdiffusion, and Exponential Decay

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Disordered Systems

Background:

• Understanding charge transport in disordered quantum systems is crucial for novel electronic devices.
• The t-V model describes interacting spinless fermions in one dimension, relevant for quantum wires.
• Disorder and interactions significantly impact electron dynamics, potentially leading to non-diffusive transport.

Purpose of the Study:

• To investigate charge relaxation dynamics in spinless disordered fermion quantum wires.
• To analyze the time-dependent density propagator and its dependence on energy density and disorder strength.
• To characterize the nature of charge transport, specifically identifying subdiffusive or diffusive regimes.

Main Methods:

• Calculation of the time-dependent density propagator (Π_{ϵ}(x,t)) for the t-V model.
• Analysis of the propagator's width (Δx_{ϵ}(t)) and its time dependence using the exponent function β_{ϵ}(t).
• Systematic variation of energy density (ϵ) and disorder strength (W) below the critical value (W_{c}).

Main Results:

• Confirmed a region exhibiting subdiffusive dynamics (β_{ϵ}(t) < 1/2), potentially transient.
• Observed that subdiffusion coexists with an enhanced return probability to the origin, decaying slower than expected for diffusion.
• Found spatial decay of the density propagator to be non-Gaussian, often exponential or slower.
• Did not confirm many-body mobility edges in reported delocalized phase regions.

Conclusions:

• Charge relaxation in these quantum wires can exhibit transient subdiffusion, deviating from conventional diffusive behavior.
• The observed dynamics are consistent with strong disorder effects and fractal Griffiths regions.
• The findings challenge existing models and highlight the complex interplay of disorder and interactions in one-dimensional systems.