Fermionic Gaussian states: an introduction to numerical approaches
Jacopo Surace, Luca Tagliacozzo
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.
Topics & Concepts
GaussianHamiltonian (control theory)Statistical physicsComputer scienceIsing modelNumerical analysisProduct (mathematics)Applied mathematicsMathematical optimizationPhysicsMathematicsQuantum mechanicsMathematical analysisGeometryQuantum many-body systemsQuantum Computing Algorithms and ArchitectureQuantum Information and Cryptography