Bifurcations and catastrophes at the boundaries separating the phases of quantum correlations

Abstract

The spin-1/2 XXZ chain in a uniform magnetic field at thermal equilibrium is considered. For this model, we give phase diagrams for the one-way quantum work deficit (thermal discord). The diagrams can contain regions with both stationary and variable (state-dependent) angles of optimal measurement. We also established a relationship between the behavior of optimal measurement angles near the boundaries separated different regions and Landau’s theory of phase transitions of the second and first kind. Namely, when crossing the boundary from a region with a stationary optimal measurement angle (0 or π/2) to the region with a variable angle of optimal measurement (0 < ϑ < π/2), quantum discord and one-way quantum work deficit experience a sudden change (“catastrophe”) in their behavior. The sudden change is accompanied by a splitting of the minimum characterizing stationary point of quantum correlation into two minima (i.e., bifurcation of the initial single minimum occurs). Such phenomena are analogous to phase transitions described within the Landau theory, or, more generally, by the mathematical formalism of catastrophe theory.