Thermal properties of a non-Hermitian system interacting with oscillator

In this work, we consider a two level $P{\sigma }_z$ pseudo-Hermitian system in contact with a thermal bath to study various thermodynamic properties. The system is realized in terms of infinitely many invariant subspaces. We find explicit solution in each subspace analytically. The quantum system undergoes a $P{\sigma }_z$ phase transition in each invariant subspace, when the non-Hermitian coupling exceeds a certain critical value (${\mu }_c$). We calculate various thermodynamic quantities and observe that these quantities show divergences exactly at the exceptional points (EPs) of the theory.