Sistemas de spins interagentes mapeáveis em férmions não-interagentes

Abstract

This is a review text on integrable systems within many-body quantum mechanics. It focuses on interacting spin systems whose Hamiltonian can be mapped via the Jordan- Wigner transform into a Hamiltonian of free fermions, and thus diagonalized. It approaches the steps to perform the transform and deals with the Ising and XY models. For the first model, it presents the exact results for the fundamental energy states and for the transition between ferromagnetic and paramagnetic phases related to the intensity of the external magnetic field. For the second model, he presents the equation for the time dependence of entanglement entropy in a spin chain and how the behaviour of entanglement entropy changes with the application of disorder in the external magnetic field, which leads the chain to a localized phase. It elaborates on open systems, coupling thermal reservoirs at the extremities of the spin chain, presenting the definitions for heat and work variation . It uses the Lindblad master equation to describe the time evolution of the density matrix state , together with the method of repeated interactions that describes the interaction between reservoir and system.