Efficient Diagonalization of Kicked Quantum Systems

TL;DR

This paper introduces a novel method combining FFT and Lanczos algorithms to efficiently diagonalize large matrices in kicked quantum systems, enabling analysis of systems with up to one million states.

Contribution

A new diagonalization technique that significantly reduces computational complexity for large kicked quantum system matrices.

Findings

Able to diagonalize matrices of size up to 10^6

Revealed intricate spectral properties of the kicked Harper model

Outperforms standard methods in efficiency and scale

Abstract

We show that the time evolution operator of kicked quantum systems, although a full matrix of size NxN, can be diagonalized with the help of a new method based on a suitable combination of fast Fourier transform and Lanczos algorithm in just N^2 ln(N) operations. It allows the diagonalization of matrizes of sizes up to N\approx 10^6 going far beyond the possibilities of standard diagonalization techniques which need O(N^3) operations. We have applied this method to the kicked Harper model revealing its intricate spectral properties.