The Landscape Law for Tight Binding Hamiltonians

The present paper extends the landscape theory pioneered in Filoche and Mayboroda (Proc Natl Acad Sci USA 109(37):14761-14766, 2012), Arnold et al. (Commun Partial Differ Equ 44(11):1186-1216, 2019) and David et al. (Adv Math 390:107946, 2021) to the tight-binding Schrodinger operator on Z(d). In particular, we establish upper and lower bounds for the integrated density of states in terms of the counting function based upon the localization landscape.

Automated summary

The present paper extends the landscape theory to the tight-binding Schrodinger operator on Z(d), providing upper and lower bounds for the integrated density of states based on the localization landscape.