Frustrazione topologica in catene di spin quantistiche: un approccio tramite la boudary effect function

Topological frustration (TF) is a weak form of frustration that can be introduced in antiferromagnetic quantum spin-1/2 chains through a combination of periodic boundary conditions and odd system sizes. Despite deriving from a choice of the boundary conditions, it has been shown that TF can deeply affect the low energy physics of these models, modifying their critical behavior (thus going beyond the paradigm of Landau theory of phase transitions) and enhancing the quantum resources of their ground states, both in terms of entanglement entropy and non-stabilizerness. In this work, we will show that the so-called boundary effect function (BEF), a quantity connected to the Uhlmann fidelity that was recently introduced as a tool for the study of boundary effects in quantum spin chains, can be used to detect the presence of topological frustration in quantum spin chains. Taking the 1D Ising chain as a reference model, we will employ both numerical and analytical techniques to show that the BEF is zero in the absence of TF, while it becomes finite in its presence.