Analytical solution for the Fermi-sea energy of two-dimensional electrons in a magnetic field: lattice path-integral approach and quantum interference

TL;DR

This paper presents an exact analytical solution for the Fermi-sea energy of 2D electrons in a magnetic field using a novel lattice path-integral approach, highlighting quantum interference effects.

Contribution

It introduces a new analytical method that maps the problem to a lattice walker, enabling exact calculation of kinetic energy in 2D electron systems.

Findings

Exact solution for 2D electron kinetic energy at half-filling

Validation of analytical results with numerical calculations

Insight into quantum interference effects in lattice systems

Abstract

We derive an exact solution for the total kinetic energy of noninteracting spinless electrons at half-filling in two-dimensional bipartite lattices. We employ a conceptually novel approach that maps this problem exactly into a Feynman-Vdovichenko lattice walker. The problem is then reduced to the analytic study of the sum of magnetic phase factors on closed paths. We compare our results with the ones obtained through numerical calculations.