Finite-temperature transport in gapless and gapped 1D integrable quantum systems

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics

Background:

• Generalized hydrodynamics (GHD) has advanced understanding of finite-temperature transport in 1D integrable models.
• Anomalous superdiffusive transport mechanisms have been explained by GHD in various systems.
• Discrepancies exist regarding finite-temperature charge transport in the 1D Hubbard model at zero chemical potential.

Purpose of the Study:

• To resolve disagreements on finite-temperature charge transport in the 1D Hubbard model at zero chemical potential.
• To clarify the role of global symmetry treatments in GHD predictions.
• To deepen the understanding of anomalous superdiffusion in 1D integrable systems.

Main Methods:

• Review of GHD and other methods for predicting spin transport in gapless 1D integrable models.
• Analysis of T > 0 transport results in gapped 1D integrable models, focusing on the 1D Hubbard model and XXZ chain.
• Identification and discussion of the origins of discrepancies in transport predictions.

Main Results:

• Controversy identified regarding whether charge transport is anomalous superdiffusive or normal diffusive.
• Disagreements linked to differing treatments of the model's global symmetry (SU(2)xSU(2) vs. [SU(2)xSU(2)xU(1)]/Z_2^2).
• Resolution of discrepancies offers deeper insights into anomalous superdiffusion.

Conclusions:

• The treatment of global symmetry is crucial for accurate predictions of charge transport in the 1D Hubbard model.
• Understanding these symmetry aspects is key to resolving debates on anomalous superdiffusion.
• This work contributes to a more unified understanding of transport phenomena in 1D integrable systems.