  A hybrid spin-electron system defined on one-dimensional double-tetrahedral
chain, in which the localized Ising spin regularly alternates with two mobile
electrons delocalized over a triangular plaquette, is exactly solved with the
help of generalized decoration-iteration transformation. It is shown that a
macroscopic degeneracy of ferromagnetic and ferrimagnetic ground states arising
from chiral degrees of freedom of the mobile electrons cannot be lifted by a
magnetic field in contrast to a macroscopic degeneracy of the frustrated ground
state, which appears owing to a kinetically-driven frustration of the localized
Ising spins. An anomalous behavior of all basic thermodynamic quantities can be
observed on account of massive thermal excitations, which mimic a
temperature-driven first-order phase transition from the non-degenerate
frustrated state to the highly degenerate ferrimagnetic state at non-zero
magnetic fields. A substantial difference in the respective degeneracies is
responsible for an immense low-temperature peak of the specific heat and very
abrupt (almost discontinuous) thermal variations of the entropy and sublattice
magnetizations.
