Thermodynamics of spinless fermion on triangular plaquettes or tetrahedral chain

The spinless fermion on triangular plaquettes or tetrahedral chain is considered in this work with hooping term, repulsive Coulomb interactions between nearest-neighbor sites and chemical potential. This is an exactly solvable model, through decoration transformation and transfer matrix approach, when the hopping term acting with nodal sites is ignored, but all other parameters considered are quite general. Five different states are shown in the phase diagrams, these states are distinguished by particle density, empty, 1, 2, 3 and 4 particles per unit cell on the triangular plaquette and one nodal site, or a tetrahedron unit cell. The boundary of these regions are frustrated state curves. The phase with particle density 2 is limited by a frustrated state curve with non-trivial residual entropy, whereas the other boundaries are limited also by frustrated state curves, but with trivial residual entropy. The existence of this non-trivial phenomenon has also been evidenced by temperature dependencies of the specific heat. The behavior of the specific heat at low-temperature is influenced by the interaction between thermal and quantum fluctuations. Finally some other additional quantities were also considered, such as the internal energy and compressibility.