Phase transition and entropy spectrum of the BTZ black hole with torsion

In this paper, we study the phase transition and the entropy spectrum of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole with torsion obtained in ($1+2$)-dimensional Poincar\'e gauge theory. By calculating the heat capacity, we find that the BTZ black hole with torsion we consider will experience phase transition at some critical point. This indicates that the critical behaviors of black holes do not only depend on the geometry of spacetime, but also have to do with the theory of gravity under consideration. In addition, we derive the entropy spectrum of the BTZ black hole according to the quasinormal modes and the adiabatic invariance. It shows that the area or entropy spectrum will also rely on the concrete gravitational action.