Indirect Band Gap Controls Density-Matrix Decay in Tight-Binding Models
A result in the mathematical analysis of electronic structure showing that the exponential off-diagonal decay of the single-particle density matrix (the 'nearsightedness' underlying linear-scaling algorithms) is governed by a material's indirect band gap rather than its direct band gap. Learners study how, in a linear tight-binding model at zero Fermi temperature, representing the density matrix in reciprocal space yields a qualitatively sharp decay-rate estimate that stays stable under perturbations and explains strong locality in small-direct-gap semiconductors.
NEARSIGHTEDNESS IN MATERIALS WITH INDIRECT BAND GAP JUERONG FENG, HUAJIE CHEN, CHRISTOPH ORTNER
A mathematical-physics study of nearsightedness (the exponential off-diagonal decay of the single-particle density matrix) in linear tight-binding models of electronic structure at zero Fermi tempera…