Majorana fermions, supersymmetry, and thermofield dynamics

We show the existence of supersymmetry and degeneracy for an arbitrary $($even or odd$)$ number of Majorana fermions without invoking any symmetry of the Hamiltonian. We analyze supersymmetry at a finite temperature using the thermofield dynamics formalism. Such an analysis emerges from the construction of a thermal formulation for Majorana fermions in the thermofield dynamics scenario. Furthermore, we derive thermal braiding operators via Bogoliubov transformations and find its action on a thermal Bell state. Based on quantum fidelity, we measure the distance between the thermal states and the corresponding pure states. In the limit as the temperature tends to zero, we recover the pure states and the fidelity approaches unity. This analysis makes it possible to analyze the influence of temperature on the evolution of the system.