Spectrum-wide quantum criticality at the Anderson-Mott transition

The interplay of interactions and Anderson localization has been studied intensively in recent years. In this work, we study the Anderson transition in interacting power-law random hopping models. These models interpolate between the random matrix and strong 1D localization limit, and the non-interacting version exhibits a “spectrum-wide quantum critical” (SWQC) metal-insulator transition (MIT), tuned by the hopping decay power. SWQC can play a role in both topological and strongly correlated superconductors [1]. Our previous numerical study demonstrated that the SWQC transition survives the incorporation of attractive Hubbard interactions, and strongly enhances Cooper pairing near the MIT [2]. Here we combine analytical and numerical approaches to determine how interactions shift the MIT, preserve or destroy SWQC, and mediate inelastic relaxation processes responsible for dephasing.

[1] J. F. Karcher and M. S. Foster, Ann. Phys. 435, 168439 (2021).

[2] X. Zhang and M. S. Foster, arXiv:2204.02996.