In this work we probe and contrast different measures of entanglement for quantum systems, the most well-known of which is the von Neumann entropy. The entropy, however, is only a good measure of entanglement when a system is in a pure state. For mixed states other measures exist such as the concurrence, the Entanglement of Formation, and Negativity. We choose to study a model Hamiltonian representing a Heisenberg spin chain in a magnetic field which provides a testbed for studying the fundamentals of entanglement.
Using QuTiP, a library for quantum computations and simulations in python, we can generate the Hamiltonian and density matrix and eventually calculate the concurrence as the primary measure of the degree of the entanglement between pairs of spins. We probe the concurrence for variations in a magnetic field, temperature, coupling constants as well as system size and boundary properties.