  The spin-1/2 Ising-Heisenberg three-leg tube composed of the Heisenberg spin
triangles mutually coupled through the Ising inter-triangle interaction is
exactly solved in a zero magnetic field. By making use of the local
conservation for the total spin on each Heisenberg spin triangle the model can
be rigorously mapped onto a classical composite spin-chain model, which is
subsequently exactly treated through the transfer-matrix method. The
ground-state phase diagram, correlation functions, concurrence, Bell function,
entropy and specific heat are examined in detail. It is shown that the spin
frustration represents an indispensable ground for a thermal entanglement,
which is quantified with the help of concurrence. The specific heat displays
diverse temperature dependences, which may include a sharp low-temperature peak
mimicking a temperature-driven first-order phase transition. It is convincingly
evidenced that this anomalous peak originates from massive thermal excitations
from the doubly degenerate ground state towards an excited state with a high
macroscopic degeneracy due to chiral degrees of freedom of the Heisenberg spin
triangles.
