Fermionic Gaussian states: an introduction to numerical approaches

TL;DR

This paper provides a practical introduction to the analysis and numerical simulation of Fermionic Gaussian states, including modern techniques, examples, and new algorithms linking them with matrix product states.

Contribution

It introduces novel algorithms connecting Fermionic Gaussian states with matrix product states, enhancing numerical methods for these systems.

Findings

Demonstrates numerical techniques using the F_utilities Julia package.

Studies the transverse field Ising Hamiltonian in detail.

Introduces algorithms bridging Fermionic Gaussian states and matrix product states.

Abstract

This document is meant to be a practical introduction to the analytical and numerical manipulation of Fermionic Gaussian systems. Starting from the basics, we move to relevant modern results and techniques, presenting numerical examples and studying relevant Hamiltonians, such as the transverse field Ising Hamiltonian, in detail. We finish introducing novel algorithms connecting Fermionic Guassian states with matrix product states techniques. All the numerical examples make use of the free Julia package F_utilities.