The Kernel Polynomial Method applied to tight binding systems with time-dependence

Abstract

The Kernel Polynomial Method (KPM) is a method to approximate any function as a polynomial of finite order. In this research the KPM will be used to approximate the density of states and expectation values of physical observables in a tight binding system. To be able to use the KPM a tight binding Hamiltonian is obtained by using the python package Kwant. A python implementation of KPM combined with a time propagator then results in time-dependent expectation values of any operator. This approach benefits from large system sizes, since KPM uses a statistical approximation that increases in accuracy with larger size. The statistical approximation always converges, but there is limited guarantee as to how fast it converges. In further research the KPM could be compared to other available approaches. Another possibility is to use the KPM to get a general overview of the system and combine it with more exact approaches to find specific results.