Capturing Mott–Anderson competition at strong coupling and strong disorder

Establish a computational and theoretical treatment of the Anderson-Hubbard model at strong on-site interaction and strong random local disorder that captures the competition between Mott insulating and Anderson insulating behaviors, enabling reliable analysis of non-equilibrium dynamics such as the out-of-time-order correlator in this regime.

Background

The interplay of strong electron correlations (Mott physics) and strong random disorder (Anderson localization) in the Anderson-Hubbard model is a central problem in condensed matter physics. The present paper employs non-equilibrium DMFT with CPA and a second-order perturbative impurity solver, which is reliable only in the weak-coupling metallic regime.

The authors explicitly note that their current approach cannot capture the competition between Mott and Anderson insulating phases at strong coupling and strong disorder, indicating an unresolved challenge for methods capable of treating this regime.

References

Unfortunately, at present we are not able to capture the competition between Mott insulator and Anderson insulator at strong coupling and strong disorder regimes.

— Out of Time Order Correlation of the Hubbard Model with Random Local Disorder (2403.03214 - Rangi et al., 5 Mar 2024) in Section 5. Conclusion