Fermionic Gaussian states: an introduction to numerical approaches

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.

Second-order statistics of fermionic Gaussian states

“…A density matrix ρ corresponds to a fermionic Gaussian state if it can be represented as the exponential of a fermionic Gaussian Hamiltonian that admits a quadratic structure [24], i.e.…”

Entanglement capacity of fermionic Gaussian states

“…. , γ2N ) † , a system of fermionic Gaussian state is then characterized by the density operator of the form [22,31] ρ(γ) = e −γ † Qγ tr(e −γ † Qγ ) ,…”

Entanglement capacity of fermionic Gaussian states

“…. , γ2N ) † , a system of fermionic Gaussian state is then characterized by the density operator of the form [22,32]…”