An Algebraic Geometry Method for Calculating DOS for 2D tight binding models

2012/05/05 by Koushik Ray, Ray, Koushik, Siddhartha Sen +1
Chemistry · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Materials Science (cond-mat.mtrl-sci) #Mathematical Physics (math-ph) #Other Condensed Matter (cond-mat.other) #Scientific Research and Discoveries #cond-mat.mtrl-sci #cond-mat.other #hep-th #math-ph #math.AG #math.MP

paper · pdf · doi:10.48550/arxiv.1205.1122

Latex. 1+10 pages. Noted that the parameter $ε$ is related to the square of the energy, rather than the energy itself. Corresponding corrections in the dispersion relations made

openalex publication_date 2012/05/05 · arxiv created 2012/06/01 · arxiv updated 2012/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An algebraic geometry method is used to calculate the moments of the electron density of states as a function of the energy for lattices in the tight binding approximation. Interpreting the moments as the Mellin transform of the density allows writing down a formula for the density as an inverse Mellin transform. The method is illustrated by working out the density function for the two-dimensional square and honeycomb lattices.

Citations

• Density of electron states in a rectangular lattice under uniaxial stress
• Picard-Fuchs equations and mirror maps for hypersurfaces

Related

• Density of states techniques for lattice field theories using the functional fit approach (FFA)
• Density matrices in O(N) electronic structure calculations: theory and applications
• QM/MM methods for crystalline defects. Part 1: Locality of the tight binding model
• Self-Consistent Equations for Nonempirical Tight Binding Theory
• Numerical computation of critical properties and atomic basins from 3D grid electron densities